Ruggero Maria Santilli

P. O. Box 1577, Palm Harbor, FL 34682

Curriculum Vitae

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Last revision March 11, 2003

REDUCTION OF MESONS AND UNSTABLE LEPTONS TO HADRONIC BOUND STATES OF ISOELECTRONS AND ISOPOSITRONS, AND ITS COMPATIBILITY WITH SU(3) CLASSIFICATIONS.

1. STRUCTURE MODEL OF THE PI-ZERO MESON WITH PHYSICAL CONSTITUENTS.

3. COMPATIBILITY OF THE PROPOSED STRUCTURE MODELS OF MESONS WITH KNOWN SU(3) CLASSIFICATIONS

*PROPOSED EXPERIMENT 4.1: TEST ANTIMATTER PHOTONS IN PION DECAYS.*

*PROPOSED EXPERIMENT 4.2: ASCERTAIN WHETHER HADRON DECAYS VERIFY OR VIOLATE ISO-SELF-DUALITY.*

6. GENERAL REFERENCES ON HADRONIC MECHANICS.

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**1. STRUCTURE MODEL OF THE PI-ZERO MESON WITH PHYSICAL CONSTITUENTS.
**

Hadronic mechanics was built for the primary purpose of **reducing all mesons and (unstable) leptons to bound states of electrons and positrons at short distances.** As it is well known, this reduction is impossible for quantum mechanics. However, as outlined in this Part IV, said reduction is quantitatively possible for the covering hadronic mechanics.

In this section we outline the structure model for the p^{o} with physical, elementary and stable constituents. The corresponding structure models for the remaining mesons and (unstable) leptons is outlined in the second section. The rather elementary compatibility of our structure models of mesons with known SU(3) classifications is outlined in the third section. New clean energies and other novel industrial applications will become possible only following the extension of the results to baryons in Part V.

The fundamental physical evidence underlying this section is that of **ball lighting**, according to which ordinary electrons can form bound states at small distances with an increasing number of constituents, a phenomenon known as **electron accretion** by the ball lighting. The structure models of mesons and (unstable) leptons presented in this Part IV can be conceived along the principle of ball lighting and its increase of mass via electron accretion although implemented with the presence of positrons as the primary origin of instabilities.

The experimental evidence of the bonding of electrons at short distances into ball lighting and their accretion of electrons has been vastly ignored by the 20-th century physics because quantum mechanics cannot explain the bonding of two (let alone many) electrons as they occur in Cooper pairs and valence bonds. Since we adapt theories to physical realities (rather than the widely used opposite approach), we first admit the physical reality of electron bonding at short distances, and construct hadronic mechanics in such as way to represent said physical reality. The reduction of all mesons and (unstable) leptons to new bound states of electrons and positrons at short distances is then a mere consequence.

The p^{o} meson admits the spontaneous decay into one electron e^{-} and one positron e^{+} with the lowest mode (see the Particle Data),

(1.1) p^{o} => e^{-} + e^{+}, mode < 10^{-8} (CL = 90%).

Therefore, the electron and the positron are assumed as the actual, physical, elementary constituents of the p^{o}, and its spontaneous decay with the lowest mode is assumed to be a tunnel effect of the constituents.

However, it is easy to prove that a quantum mechanical (qm) model of the p^{o} as a bound state of one electron and one positron is IMPOSSIBLE, and we shall write

(1.2) p^{o} ≠ (e^{-},e^{+})_{qm}.

This is due to the following reasons:

1) Quantum mechanical model (1.2) is not able to represent the size (charge radius) of the p
^{o}, since the ONLY quantum bound state of one electron and one positron is the **positronium** with the charge radius of the order of 10^{-8} cm, while the charge radius of the p^{o} is R = 10^{-13} cm;

2) Quantum mechanical model (1.2) is not able to represent the meanlife of the p^{o} t =
0.8 x 10^{-16} sec, since the smallest predicted meanlife is that of the positronium in the ^{1}S state, that is of the order of 10^{-10} sec;

3) Quantum mechanical model (1.2) cannot represent the rest energy of the p^{o}, E_{po} = 134.97 MeV, because the sole bound states predicted by quantum mechanics are those with **mass defects** due to **negative binding energies,** in which case the maximal rest energy can only be that of 2xm_{e} = 1.02 MeV.

In view of these and other inconsistencies, the hypothesis that the electron and the positron are the actual physical constituents of the p^{o} was abandoned soon after its discovery, and this lead to the conjecture that the unobservable quarks are the physical constituents of the particle.

However, quarks cannot be even defined in our spacetime, let alone observed, and have a host of additional inconsistencies when assumed as the actual, physical, "elementary" constituents of hadrons outlined in part in Section II. For this reason, R. M. Santilli (23,38), then at Harvard University under DOE support, proposed in 1978 the construction of a generalization of quantum mechanics under the name of **hadronic mechanics** for the specific purpose of resolving insufficiencies 1), 2) and 3) in such a way that the electron and the positron can be assumed as the actual physical constituents of the p^{o}.

In plain language, rather than adapting physical reality to pre-existing theories, the task of building hadronic mechanics was that of adapting the theories themselves to physical reality.

The latter objective was achieved in full already in the original proposal (38), Section 5.1, pages 827-879 (reproduced in the pdf file at the end of this section) where one can see **THE ACHIEVEMENT OF THE EXACT REPRESENTATION OF THE TOTALITY CHARACTERISTICS OF THE p ^{o} AS A BOUND STATE OF ONE MUTATED ELECTRON AND ONE MUTATED POSITRON.** The name used in Ref. (38) for ,mutated electrons was that of "eletons." The terminology that became established in the subsequent years is that of

(1.3) p^{o} = (e^^{-},e^^{+})_{hm}

With the passing of the decades, the original model (38) of 1978 has remained fully valid, both in conception and quantitative treatment (although mostly ignored in favor of conjectural constituents that cannot be even defined in our spacetime). The main contribution that occurred in subsequent years has been the proof of the INVARIANCE of hadronic mechanics, namely, the invariance of the numerical predictions under the time evolution of the theory without which all models have no physical or mathematical value (see the catastrophic inconsistencies of generalized theories of Theorem II.2.1). Therefore, in this section we shall review model (38) with the sole upgrade of the terminology that was finalized during the past two decades.

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The first necessary condition to achieve a consistent model (1.3) is to exit from the class of equivalence of quantum mechanics, trivially, because quantum mechanics CANNOT achieve such a consistent representation. This can be done in a variety of ways. That suggested in the original proposal (38), and still fully valid today (see the review in Section II.3), is the use of a **nonunitary transform of the positronium model.**

Consider the **Schroedinger equation for the positronium** essentially given for one electron with mass m and charge -e and state |e> = |e(t, r)> in the field of the positron with charge +e and the same mass m,

(1.4a) H x |e> = (pxp/2m - e^{2} / r) x |e> = E_{o} x |e>,

(1.4b) p x |e> = - i x h x D_{r} |e>,

where h represents h-bar and, due to insufficient symbols in the HTLM format, D_{r} represents partial derivative with respect to r, and magnetic interactions are generally ignored due to the long range character. The image of the above equations under a nonunitary transform is given by

(1.5a) U x U^{+} = I^ = 1 / T ≠ I, I^ > 0,

(1.5b) (U x U^{+})^{-1} = T,

(1.5c) U x (H x |e>) = (U x H x U^{+}) x (U x U^{+})^{-1} x (U x |e>) = H^ x T x |e^> = H^*|r^> = E^*|e^> = E x |e^>,

(1.5d) U x (p x |e>) = (U x p x U^{+}) x (U x U^{+})^{-1} x (U x |e>) = p^ x T x |e^> = p^*|e^> = - i x h x U (D_{r} |e>) = - i D^_{r} |e^> = - i x h x I^ x D_{r} |e^>,

where |e^> = |e^(t, r)> represents the wavefunction of the **isoelectron**, and D^_{r} represent partial isoderivative (Part I).

Eq. (1.5c) constitutes the **structure equation of the p ^{o} meson in the iso-Euclidean space E^(r^, d^, R^) over the field R^ of isoreal numbers n^ = nxI^,** and can be written

(1.6a) H^*|e^> = [(- h^^{2}^ / m^)*p^*p^ + V^_{Coul}]*|e^> = E^*|e^>

(1.6b) p^*|e^> = - i x h x D^_{r} |e^>,

(1.6c) V^_{Coul} = (N / r) x I^,

(1.6d) m^ = m x I^,E^ = E x I^, h^ = h x I^,

where the * product (first introduced in Ref. (38)) is given by A*B = AxTxB, V^ is an isofunction (thus, it is multiplied by I^ because with values on R^) and m^ and E^ are isoscalars (thus with the structure m^ = mxI^, E^ = ExI^).

The Coulomb force (1.6c) is left with an undetermined sign, because we do not know whether the sum of the attractive Coulomb force due to opposite charge and the repulsive Coulomb force due to parallel magnetic moments (see Figure 1) is attractive or repulsive at mutual distances of 1 F. As we shall see in a moment, this issue is irrelevant because the strong nonpotential force is such to absorbs Coulomb force (1.6c) irrespective of its sign, and still produce a strongly attractive force. Note also that the Coulomb force between the magnetic moments is generally ignored in the positronium, but it cannot be any longer ignored at distances of the order of 1 F since it can acquire very large values.

Note that** Eq. (1.6a) formally coincides with the structure equation of the positronium by conception and construction,** although it is written on isospace over isofields. This feature is expected by experts on isotopies because the main difference between the conventional equation for the positronium and that for the p^{o} is the addition of nonpotential forces represented by the isounit I^ and the isomultiplication AxTxB. At the abstract level, I^ and I as well as A*B = AxTxB and AxB coincide (because I^ = 1/T is positive definite by assumption), thus resulting in the indicated formal identity, a general rule for all hadronic models.

Eq. (1.5a) can be explicitly written after elimination of terms such as I^*A = (1/T)xTxA = A

(1.7) H^ x T x |e^> = [(1/m)xp^xTxp^xT + (N / r)] x |e^> = E x |e^>

In order to obtain an explicit structure equation for the p^{o} we have to work out its **projection** on our conventional Euclidean space E over the conventional field R. It will be only at that point that nonpotential contributions will appear explicitly. For this purpose we study the term

(1.8) (1/m) x p^ * p^ * |e^> = - (h^{2} / m) x D^_{r} D^_{r} |e^>,

that, by using Eq. (1.5d), can be written

(1.9) - (h^{2} / m) x D^_{r} D^_{r} |e^> = - (h^{2} / m) x I^ x D_{r} x I^ x D^_{r} |e^> = - (h^{2} x I^^{2} / m) x D_{r} D_{r} |e^> - (h^{2} x I^ x k / m) x (D_{r} I^) x |e^>,

where k is the conventional eigenvalue of p.

At this point it is necessary to make an explicit selection of the isounit I^. For that purpose, remember that, by basic assumption, hadronic mechanics must recover quantum mechanics at distance sufficiently bigger than the size of the p^{o} (38). This is easily achieved via the condition for all realizations of the isounit

(1.10) Lim I^_{r>>1F} = I.

The latter condition can be easily verified with a realization of the type

(1.11a) I^ = exp[(e^_{up}|x|e^_{down}) x F(r)],

(1.11b) (e^^{-}_{up}|x|e^^{+}_{down}) = Integral {[(e^_{up}^{-}(r)]^{+} x e^_{down}(r) d^{3}r.

Whenever the overlapping of the wavepackets is zero, integral (1.11b) is null, the exponent in exponential (1.11a) is null, I^ recovers the trivial value I, and quantum mechanics is uniquely and identically recovered.

The selection of the function F(r) must be such to generate a strongly attractive force because, in its absence, the main objections 1), 2) and 3) cannot be resolved. The original selection was such that the projection in our spacetime of the nonpotential force yields a strongly attractive Hulten potential (Eq. (5.1.6), page 833, Ref. (38)). Even though other selections are possible, the original selection is still the best for various reasons indicated below. This implies the selection of the isounit

(1.12) I^ = exp{- [r x e^{- r / R} / (1 - e^{- r / R})] x
(e^^{-}_{up}|x|e^^{+}_{down})},

where R is the charge radius of the p^{o}. After solving the structure equation, the above expression can be also written

(1.13) I^ = exp[- (|e> / |e^>) x
(e^^{-}_{up}|x|e^^{+}_{down})],

|e> is the wavefunction of the ordinary electron in the positronium and |e^> is the wavefunction of the isoelectron in the p^{o}.

Note that isounit (1.13) represents precisely the main interactions of hadronic mechanics because they are nonlocal-integral (in view of integral (1.11b), nonlinear (because depending on the wavefunction in a nonlinear way) and nonpotential (because not describable with a potential or a Hamiltonian, the Hulten potential being a mere projection.

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Following selection (1.13), expression (1.9)) becomes

(1.14) - (h^{2} x I^^{2} / m) x D_{r} D_{r} |e^> - (h^{2} x I^ x k / m) x (D_{r} I^) x |e^> = - (h^{2} / m') x D_{r} D_{r} |e^> + V_{Hulten>} x |e^>,

where

(1.15) V_{Hulten} = - K x e^{- r / R} / (1 - e^{- r / R}),

plus additional terms proportional to R and its powers that, as such, can be ignored due to the small value of R. In Eq. (1.15) the minus sign of the Hulten potential represents **attraction.** Note that** the Hulten potential does not exist on isospaces over isofields.** In fact, it only emerges in the approximation of the **projection** of the true structure equation (1.6a)_ in our spacetime.

An important feature of Eq. (1.14) is another general law of hadronic mechanics identified since the original proposal, namely, the **mutation of the rest energy of the electrons** m => m' (Eq. (5.1.9), p. 834, Ref. (38)), also called in more recent language the **isorenormalization of the rest energy of the electron into that of the isoelectron.** Such a mutation can be essentially reached for the elementary level of this presentation via the average

(1.16) m' = m / Aver. (k x I^),

where the average is done within the charge radius R. More technically, the above isorenormalization is characterized by the isotopies of conventional renormalization procedures, those lifted for a nontrivial value of the unit. The latter aspect is not presented because excessively advanced for the limited scope of this presentation.

The mutation m => m' is **necessary** for consistency, because the Schroedinger equation admits consistent solutions only for **negative binding energies** (otherwise, for positive binding energies the indicial equation becomes inconsistent and no bound state is possible).

Equivalently, in the absence of the mutation m => m', the binding energy of model (1.3) should be positive (because the mass of the meson is much bigger than the sum of the mass of the electron and that of the positron). The isorenormalization here considered is, therefore, crucial for consistency and illustrates the necessity of the notion of **isoparticle** for our model of the p^{o}.

Eq. (1.7) can then be written

(1.17) [- (h^{2} / m') x D_{r} D_{r} + V_{Coulomb} + V_{Hulten>}] x |e^> = E x |e^>,

where V_{Coulomb} is now an ordinary function (that is, no longer multiplied by I^). But, as it is well known, the Hulten potential behaves like the Coulomb one at short range,

(1.18) V_{Hulten r<< 1F} = - K / r.

Therefore, **the Hulten potential absorbs all Coulomb potentials**, as identified since the original proposal (see Eq. (5.1.15) page 836, Ref. (38)). To a good approximation, we can only consider the Hulten potential and merely change its constant K into the value

(1.19) V = K - N.

resulting in the final equation

(1.20) [- (h^{2} / m') x D_{r} D_{r} - V x e^{- r / R} / (1 - e^{- r / R}) ] x |e^> = E x |e^>.

At this point, to achieve a consistent model, **we must represent ALL the characteristic of the p ^{o} that are:**

(1.21a) Rest energy m_{po} = 135 MeV,

(1.21b) Meanlife t_{po} =
0.8 x 10^{-16} sec,

(1.21c) Charge radius R_{po} = 1 F = 10^{-13 } cm.

(1.21d) Charge C_{po} = 0

(1.21e) Charge Parity_{po} = +,

(1.21f) Space Parity_{po} = -

(1.21g) Magnetic and Electric Dipole and Quadrupole Moments M_{po} = 0.

The null charge and spin of the where R is the charge radius of the p^{o} are easily represented by model (1.3) because of the isoelectron-isopositron structure in singlet coupling with J = 0, and they need no differential equation.
Equally trivial is the interpretation of the positive charge parity. The interpretation of the negative space parity is rather complex, inasmuch as it requires the isotopic lifting of quantum field theory that has not been initiated to date. Therefore, in Ref. (38), page 845), a similar approach was proposed in Ref. (38) by assuming that the isoelectron and the isopositron have **imaginary parity,** in which case the space parity is i^{2} = -1. In fact, it is known in conventional quantum field theories that, when the total angular momentum is null. particles can have either positive or imaginary parity, and this feature is certainly expected to persist under isotopy.

A simple interpretation of the null value of electric and magnetic dipole and quadrupole moments can be reached from the null value of the charge as well as the very small value of the distance of the p^{o} constituents. However, at a deeper level the problem is far from trivial because, as indicated in Figure 1, magnetic moments of electron and positron in singlet coupling are parallel. As a result, a deeper representation of the null values of the electric and magnetic moments (assuming that they are indeed truly null...) requires deep mutations of the intrinsic moments of each constituent when in conditions of total mutual penetration as in Fig. 1 (see Part V for an elaboration for the case of the neutron that is also applicable here).

Therefore, we remain with the representation of characteristics (1.21a)-(1.21bc) via one single structure equation in our spacetime. By using a known nonrelativistic expression for the meanlife of particle-antiparticle systems, we reach in this way the **STRUCTURE EQUATION FOR THE p ^{o} PROJECTED ON CONVENTIONAL SPACES OVER CONVENTIONAL FIELDS**, first reached in Eqs. (5.1.14), page 836, Ref. (38)

(1.22a) [- (h^{2} / m') x D_{r} D_{r} - V x e^{- r / R} / (1 - e^{- r / R}) ]] x |e^> = E x |e^>.

(1.22b) E_{po} = 2 x E_{Kin,e^} - | E | = 135 MeV,

(1.22c) t_{po}^{-1} =
4 x p x l^{2} x | e^(0)|^{2} x a x E_{Kin, e^} / h = 10^{16} sec^{-1};

(1.22d) R_{po} 10^{-13 } cm,

where l and h represents l-slash and h-bar.

The above structure equations were solved analytically in Ref. (38), including the necessary boundary conditions, etc. Unfortunately, the limitations of symbols for the HTLM format prevent its review here, and we have to refer interested reader to the pdf file at the end of this section, pages 836-843, and restrict ourselves here only with the main results.

said analytic solution also explains the reinterpretation (1.13) of isounit (1.12). In fact, it shows that |e^> behaves asymptotically like [1 - exp (1 - r/R)]/r, while |e> is known to have the asymptotic behavior exp(-r/R), thus yielding re-interpretation (1.13).

The energy spectrum of Eq. (1.22a) resulted to be, as expected, the typical spectrum of the Hulten potential

(1.23a) E = - (m' x R^{2} x V / h^{2} x n - n)^{2} x h^{2} / 4 x m' x R^{2},

(1.23b) n = 1, 2, ...., N = maximal integer in m' x R^{2} x V / h^{2} x n

Note that **the Hulten potential has a FINITE number of admissible energy levels,** as it is well known.

The numerical solution was expressed in terms of the following two parameters (that are NOT arbitrary as typical in manipulations of data, and are instead an integral part of the ANALYTIC SOLUTION)

(1.24a) E_{Kin,e^} = k_{1} x h x c / R = h^{2} / 2 x m' x R^{2},

(1.24b) m' x V x R^{2} / h^{2} = k_{2} = 1 +
e, 0 < = e < 1,

where 0 < = e < 1 originates from the boundary conditions. In this case the Hulten constant becomes

(1.25) V = k_{2} x h^{2} / m' x R^{2} = 2 x k_{2} x E_{Kin,e^} = 2 x E_{Kin,e^},

because k_{2} is very close to 1. As we shall soon see, the above expression establishes that the value of V is rather large. In turn, this establishes the strength of the strong nonpotential interactions.

In terms of the above parametrization we have

(1.26) E_{po} = 2 x E_{Kin,e^1} x [ 1 - ( k_{2} - 1 )^{2}] x h x c / R = 135 MeV.

Following due analytic process we cannot possibly review here, the set of structure equations (1.22) is then reduced to the following algebraic solution in the k-parameters (Eq. (5.1.32, page 840, Ref. (38))

(1.27a) k_{1} x [ 1 - ( k_{2} - 1 )^{2}] = E_{po} x R / 2 x h x c,

(1.27b) ( k_{2} - 1 )^{3} / k_{1} = 48 x 137^{2} x R / 4
x p x c x t_{po}.

with numerical results

(1.28a) k_{1} = 0.34,

(1.28b) k_{2} = 1 + 4.27 x 10^{-2}.

It then follows that **THE HADRONIC STRUCTURE EQUATIONS (1.22) ACHIEVE A NUMERICAL, EXACT AND INVARIANT REPRESENTATION OF THE "TOTALITY" OF THE CHARACTERISTICS OF THE p ^{o} MESON.**

Moreover, under numerical solution (1.27), spectrum (1.23) becomes

(1.29) E = - [ ( 1 + 4.27 x 10^{-2} ) / n - n ]^{2} x ( 1 + 4.27 x 10^{-2} / 4 x V.

It then follows that **HADRONIC MECHANICS SUPPRESSES THE POSITRONIUM SPECTRUM DOWN TO ONLY ONE SINGLE ENERGY LEVEL, THAT OF THE p ^{o}.** This is a

In fact, for any possible excited state, the overlapping of the wavepackets of the isoelectron and isopositron is null, the isounit recovers the conventional value I and the positronium model is recovered identically by structure equations (1.22). Therefore, **ALL EXCITED STATES OF THE p ^{o} ARE THE STATES OF THE POSITRONIUM.**

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We remain with the identification of the reason why the iso-Schroedinger's equation is consistent (resolution of inconsistency 3)). This was done in Eqs. (5.1.34)-(5.1.37), page 842, Ref. (38), with the results

(1.30) Max. Rest Energy Mutation E_{Tot,e^} = m' x c^{2} = 68 MeV,

as well as the value

(1.31) E = - (4.27 x 10^{-2})^{2} x ( 1 + 4.27 x 10^{-2} / 4 x V = 0,

where the symbol = stands for approximate value. The very low value of the binding energy confirms the nonpotential character of our realization of the strong force. The isorenormalized value of the rest energy of the constituents confirms the selection of electrons and positrons as the ONLY known stable, massive and elementary particles compatible with Eq. (1.30).

Another peculiarity of model (1.3), also identified in the original proposal (38), page 841, is that **the positronium orbits are elliptic, while the sole orbit admitted for the stability of the p ^{o} is the TWO CONSTITUENTS ORBITING BOTH IN A CIRCLE WITHOUT THE KEPLERIAN CENTER.** In the positronium the constituents orbit in vacuum at large mutual distances according to the Keplerian structure. By comparison, in the p

The experimentally sure decays of the p^{o} are

(1.32a) p^{o} => g + g, 98.79 %

(1.32b) p^{o} => e^{-} + e^{+} + g, 1.19 %

(1.32c) p^{o} => e^{-} + e^{+} + e^{-} + e^{+}, 3.14 x 10^{-5},

(1.32d) p^{o} => e^{-} + e^{+}, 7.5 x 10^{-8},

plus decays implying the emission of hypothetical neutrinos that are "experimental beliefs" in this author's opinion because the emission of electron and positrons has been experimentally detected, while the emission of neutrinos is merely conjectured without any direct experimental verification, specifically, for the decays here at hand, thus the latter remain conjectural on strict scientific grounds outside academic politics and famous prizes (see Part V for the reasons).

The interpretation of decays (1.32) was also reached in the original proposal, Ref. (38), page 843. The first decay (1.32a) is easily interpreted via elliptic orbits that cannot be excluded as perturbations from the environment of the circular orbit, resulting in said annihilation. Decay (1.32b) is clearly due to one of the gs of the preceding decay creating an electron-positron pair. Decay (1.32c) is explained when both gs create said pairs. Decay (1.32d) is the fundamental one for model (1.3) since it represents the tunnel effect of the constituents.

Needless to say, specific calculations on these decay, if conducted with "quantum" rules, lead to a host of inconsistencies, thus demanding, again, the use of the covering hadronic rules. For instance, the calculations for the familiar process

(1.33) g => e^{-} + e^{+}

are fundamentally flawed if used in our case, trivially, because the creation occurs within a dense hadronic medium. Therefore, the correct calculations should be done for the corresponding hadronic processes

(1.34a) g => e^^{-} + e^^{+}

(1.34b) e^^{-} => e^{-} + g

(1.34c) e^^{+} => e^{+} + g^{d}

where one should note the recent prediction (21) that the photon emitted by the isopositron is the **isodual photon,** rather a conventional photon, with physical characteristics different than those of the ordinary photon. For instance, g experiences **gravitational attraction** in the field of Earth, while g^{d} is predicted to experience **gravitational repulsion.** After all, the all gs in decays (1.32) have been BELIEVED to be identical until now, without any experimental verification. Therefore, such an assumption is an "experimental belief" at this writing.

In summary, the use of quantum mechanics does not permit the identification of the constituents of the p^{o} with physical particles. On the contrary, **the use of the covering hadronic mechanics for the quantitative treatment of the contact, zero-range interactions due to deep mutual overlappings of the wavepackets permits the following results:
**

**
I) The identification of the constituents of the p ^{o} with the physical electron and positron, although existing in a mutated state due to isorenormalizations caused by said contact interactions;
**

**
II) The numerical, exact and invariant representation of ALL the characteristics of the p ^{o},**

(1.35a) Rest energy m_{po} = 135 MeV,

(1.35b) Meanlife t_{po} =
0.8 x 10^{-16} sec,

(1.35c) Charge radius R_{po} = 1 F = 10^{-13 } cm.

(1.35d) Charge C_{po} = 0

(1.35e) Charge Parity_{po} = +,

(1.35f) Space Parity_{po} = -

(1.35g) Magnetic and Electric Dipole and Quadrupole Moments M_{po} = 0,

**III) The numerical interpretation of all experimentally certain decays, although under isotopic and isodual re-interpretation,**

(1.36a) p^{o} => g + g^{d}, 98.79 %

<1.36b) p^{o} => e^{-} + e^{+} + g, 1.19 %

(1.36c) p^{o} => e^{-} + e^{+} + e^{-} + e^{+}, 3.14 x 10^{-5},

(1.36d) p^{o} => e^{-} + e^{+}, 7.5 x 10^{-8},

In closing we would like to indicate that a deeper study of decays (1.32) via hadronic mechanics requires the isotopies of quantum electrodynamics and, most importantly, **the isotopies of Feynman's diagrams.** We would like to indicate here that this study was never done in the two decades passed since Ref. (38) because of the extreme repulsion, if not sheer hysteria, by the physics community at the sole mention of improving Feynman's diagrams.

However, such a political posture can only lead to scientific obscurantism. In fact, as we shall see in Part V, the conjecture on the existence of the hypothetical neutrinos is a direct consequence of the Feynman's diagrams and, more particular, of the point-like abstraction of hadrons that is inherent in said diagrams. As soon as such an abstraction is abandoned, and hadrons are admitted as they are in the physical reality (extended, nonspherical and deformable), the conjecture of the hypothetical neutrinos becomes un-necessary under the full verification of all total conservation laws, of course.

The isotopic lifting of Feynman's diagrams is suggested to interested scholars whenever when the current, manifestly ascientific, conduction of science is hopefully replaced by future generations with a real scientific process that can only exist under a real scientific democracy for qualified inquiries, with priority in the support, rather than the current "disqualification" of qualified doubts on the terminal character of the basic knowledge of the time.

We now pass to the outline of the structure model of **unstable leptons** and of the remaining **light unflavored mesons** according to the basic rule for which hadronic mechanics (38) was built for, that **the constituents of unstable particles are physical, massive isoparticles produced free in the spontaneous decays generally those with the lowest mode.**

Following the study of the p^{o} of the preceding section, and by ignoring at this time the classification of the endless number of unstable particles identified until now (called the "particle zoo"), it is best to consider next the structure model of the structure of the muon µ^{±}.

The main characteristics of the muon are:

(2.1a) Rest Energy_{µ±} = 105.66 MeV,

(2.1b) Mean life _{µ±} = 2.19 x 10^{-6} sec,

(2.1c) Magnetic Moment_{µ±} = 1.0011 µ_{e},

(2.1d) Electric Dipole Moment_{µ±} = 3.27 x 10^{-19} ecm.

(2.1.e) Charge Radius_{µ±} = assumed to be null.

The well established decays of the muon are:

(2.2a) µ^{±} => e^{±} + neutrinos, 98.6%,

(2.2b) µ^{±} => e^{±} + g + neutrinos, 1.4 %,

(2.2c) µ^{±} => e^{±} + e^{+} + e^{-} + neutrinos, 3.4 x 10^{-5},

(2.2d) µ^{±} => e^{±} + e^{+} + e^{-}, < 10^{-12},

and other decays not relevant for our analysis, where, to separate real science from academic politics, one should never forget that **the electrons are physically detected in the above decays, while the neutrinos are conjectural,** evidently because they have never been experimentally detected, specifically, for the muon (as well as other) decays. At any rate, there exist alternative theories that verify all conservation laws without the conjecture that the various neutrinos (and their unsuccessful oscillations) are physical particle (see Part V).

The structure model of the muon proposed in Ref. (38) is based on the following main points:

1) Since the muon admits spontaneous decays, it has a composite structure;

2) The spontaneous decay are a clear indication of a particle-antiparticle annihilation process in the interior of the muon; and

3) From decays (2.2d) with the lowest modes, hadronic mechanics predicts that the muon is a bound state of three electrons at short distances, and we write (Eq. (5.2.1), page 851, Ref. (38))

(2.3) µ^{±} = (e^^{-}, e^,e^ ^{+})_{hm,J = 1/2},

where one should note the appearance of the **quantum constraint** that the resulting bound state possesses the quantum total angular momentum J = 1/2.

Model (2.3) was solved analytically in the original proposal (38), Section 5.2, by achieving ** the exact and invariant representation of ALL characteristics of the muons µ ^{±}** along the following main lines.

First, Ref. (38) performed an **isotopy of Schroedinger's equation for the helium.** This resulted in the hadronic structure model (2.3) as a **three-body system** with a dominating Hulten-type potential among each pair of constituents. Being three-body, the model admits no exact analytic solutions. However, the condition that each pair of constituents is coupled in singlet excludes as unstable all possible configurations, except the "linear" one of Figure 4, with the peripheral electrons constrained to rotate in a circular orbit. In particular, via the use of the "gear model" of Figure 2, it is instructive for the interested reader to see that the alternative configuration in which all three electrons are coupled and have the same distance from the center of the system is highly unstable.

Under said "linear" structure, model (2.3) was reduced in Ref. (38) to a special form of a ** restricted three body problem,** and solved analytically resulting in the indicated representation of all characteristics of the muons. In particular, the characteristic k-parameter of the analytic solution resulted to have the values

(2.4a) k_{1} = 2.62 x 10^{-7},

(2.4b) k_{2} = 1 + (2.98)^{1/6} x 10^{-4},

that should be compared with the corresponding values (1.28) for the p^{o}.

Note that, since k_{2} is bigger than, but very close to 1, **structure model (2.3) also suppresses the atomic spectrum of the helium down to one single energy level, that of the muon.** It was noted in Ref. (38) that the value (2.4b) was computed for the charge radius of the muon R = 10^{-19} cm and that

(2.5) R => 0 implies k_{2} => 1.

The rest energy of the muon, as well as other features, such as the differences in magnetic and electric dipole moments between muons and electrons was interpreted via a mutation of the central isoelectrons e^^{±}, thus confirming the need for hadronic mechanics.

The dominance of decay (2.2a) is easily explained via the annihilation of an isoelectron-isoproton pair, leaving the residual electron or positron isolated in vacuum, thus re-acquiring its quantum features (see Part V for the conjecture of the neutrinos). Decay (2.2d) is the tunnel effect of the constituents as indicated earlier. The other decays are interpreted via similar procedures.

******************************************

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The next unstable particle considered in Ref. (38) based on the increase of the mass was the p^{±}, whose characteristics are:

(2.6a) Rest Energy_{p±} = 139.57 MeV,

(2.6b) Mean Life_{p±} = 2.6 x 10^{-8},

(2.6c) Charge Radius_{po} = 10^{-13} cm.

The main decays of the particle are:

(2.7a) p^{±} => µ^{±} + neutrino, 99.98 %,

(2.7b) p^{±} => e^{±} + neutrino, < 10^{-4},

(2.7c) p^{±} => e^{±} + g + neutrino,

plus other decays inessential for this study.

The main hypothesis of Ref. (38) based on the above data was that the p^{±} has the following structure

(2.8) p^{±} = (e^^{-},e^^{±},e^^{+})_{hm,J=0} = (p^{0},e^^{±})_{hm,J=0}.

In the transition from the structure of the p^{o} and µ^{±} to that of the p^{±} there is a truly fundamental novelty: **the need for a necessary mutation of the spin, ** evidently because three particles with quantum spin 1/2 cannot yield a bound state with spin 0 according to quantum mechanics.

The solution suggested in Ref. (38) without elaboration (because the isotopies of SU(2)-spin had not yet been studied at that time) was that of assuming an isoelectron-isopositron pair as constituting the p^{o}, with the third isoelectron orbiting in the exterior under the condition that its total angular momentum is null (see Figure 5). This assumption is still fully valid as of today, following extensive studies on the isotopies of SU(2)-spin [4].

In essence, the familiar **spin-orbit interactions** of the large mutual distances of the atomic structure becomes dramatically stronger under conditions of mutual penetration, to such an extent of constraining the value of the spin to coincide with the orbital angular momentum, as one can easily see, again, via the :"gear model" of Figure 2. This problem is the central one for the structure of the neutron of the next Part V. Therefore, we defer the quantitative treatment via the isotopies of SU(2) to the next section.

By reducing the three-body model (the first in Eq. (2.8)) to the two-body form (the second model in Eq. (2.8)), Ref. (38) provided another exact analytic solution resulting again in the **exact, numerical and invariant representation of the totality of the characteristics of the p ^{±},** In particular, Ref. (38) found the following values of the characteristic k-quantities

(2.9a) k_{1} = 3.49 x 10^{-3},

(2.9b) k_{2} = 1 + (3.97)^{1/6} x 10^{-6},

that should be compared with values (1.28) and (2.4).

Primary decay (2.7a) is considered the strongest evidence in support of both models (2.3) and (2.8). In fact, nonquantum spin-orbits couplings are unstable, thus implying the dominance of a decay process into structure (2.3) where there is no such strong spin-orbit coupling. The interpretation of the remaining decays is also elementary (38), and will not be considered here for brevity.

,

Note that **the number of constituents INCREASE of one unit in the transition from the STRUCTURE of the p ^{o} to that of the p^{±}, while they remain the same in their CLASSIFICATION.** As we shall see, these seemingly dissonant occurrences are beautifully compatible with each other.

**********************************************

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The next structure model considered in Ref. (38) is that for the K^{o} with 497.67 MeV, that was characterized by the hadronic bound state

(2.10) K^{o} = (pp^,p^{o}^)_{hm} = (p^{+}^,p^{-}^)_{hm},

where one should note the isoparticle character of the p-mesons.

The above model was not solved analytically in Ref. (38) and its solution is left to the interested reader. An exact analytic solution is indeed possible because model (2.10) can be considered as a two-body system, in which case the analytic solution available in Section 1 applies, resulting in new values of the k-quantities in which k_{2} is expected to be closer to 1, thus **suppressing again the atomic energy spectrum down to only one energy level, that of the K ^{o}.**

Without entering into the analytic solution, a few comments are in order. In the transition from the 3-body to the 4-body hadronic bound system of electrons and positrons a number of new features occur. First, there is a new type of **axial bonding of the p-particles, a typical behavior of electrons in the formation of ball lighting.** We are referring to the bonding of identical p along their cylindrical symmetry axis, as compared to the **planar bonding of electrons** as typical for valence bonds (see Figure 3).

We also have **the equivalence between mutated p^ ^{o} and mutated p^^{±} due to the mutation of the charge.** The fluctuations between p^

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*******************************************

The next model that can also be solved analytically in first approximation is given by

(2.11) K^{±} = (K^^{o},e^^{±})_{hm},

where the single isoelectron is assumed to cause instabilities with two two bonded p^-particles, with the consequential decrease of the energy level of the K^{o}.

*******************************************

*******************************************

Additional structure model of mesons with progressively increasing rest energy that can be solved analytically (because treatable as two-body systems) are given

(2.12a) h = (K^^{o},p^^{o})_{hm},

(2.12b) r = (K^^{+},K^^{-})_{hm},

(2.12c) h' = (r^,p^^{o})_{hm},

\

and so on. The detailed study of the reduction of ALL mesons and (unstable) leptons to hadronic bound states of isoelectrons and isopositron is left to the interested reader.

The reader can now recognize the conception indicated at the beginning of Section 1, namely, that the above reduction of mesons and (unstable) leptons to bound states at short distance of a progressively increasing number of electrons and positrons is patterned along the experimental evidence of ball lighting and theor electron accretion.

**3. COMPATIBILITY OF THE PROPOSED STRUCTURE MODELS OF MESONS WITH KNOWN SU(3) CLASSIFICATIONS.
**

The compatibility of the structure model of mesons with physical, massive, stable and elementary constituents and the SU(3) classifications is so simple to appear trivial, although it requires novel mathematical knowledge without which no real advance is possible.

The compatibility was proposed in memoir (31), Section 3.15, page 715, and can be expressed as follows. First, recall that the number of **elementary** constituents is different for different mesons. Nevertheless, all members of the meson octet can be reduced to **two-body bound states,** thus recovering the two-body character of the quark model. Nevertheless, the constituents are generally **composite** and vary from particle to particle.

To achieve full compatibility, consider again the octet of light unflavored mesons and its conventional, well known representation via quarks and antiquarks where the numbers in between brackets refer to rest energies in MeV and the upper sign "-" denotes antiquarks

(3.1a) p^{+}(140), |ud^{-}>,

(3.1b) p^{o}(135), |dd^{-} - uu^{-}>,

(3.1c) p^{-}(140), |ud^{-}>,

(3.1d) h(549), |dd^{-} + uu^{-}>,

(3.1e) K^{+}(494), |us^{-}>,

(3.1f) K^{o}(498), |ds^{-}>,

(3.1g) K^{-}(494), |u^{-}s>,

(3.1h) K^{-o}(498), |d^{-}s>,

(3.1i) h'(958), |ss^{-}>.

A basic implication of hadronic mechanics is that different hadrons are characterized by different isounits. For instance, for the p^^{o} we have the total isounit

(3.2) I_{p^o} = I^_{e^+} x I^_{e^-},

for the p^{±} we have the different total isounit

(3.3) I^_{p^±} = I^_{po} x I^_{e±},

and so on. Therefore, we have the following **total isounit of the octet of unflavored mesons**

(3.4) I^_{Tot,Oct} = (I^_{p+(140)}. I^_{po(135)}, I^_{p-(140)}, I^_{h(549)}, I^_{K+(494)}, I^_{Ko(498)}, I^_{K-(494)}, I^_{K-o(498)}, I^_{h'(958)}).

It is easy to see that the above total isounit is **multivalued,**thus requiring the use of the **hypermathematics** (14) [6]. As suggested in memoir (31), compatibility between the proposed structure model of hadrons with physical, massive, stable and elementary constituents is then achieved by constructing the hypersymmetry SU(3)^ characterized by hyperunit (3.4).

It is easy to see that such a form of SU(3)^ and the conventional SU(3) are isomorphic because hyperunit (3.4) is positive-definite. Thus, all results occurring for SU(3) also occur for the hyperstructure SU(3)^. However, there is the advantage of much greater internal degrees of freedom for the resolution of the existing and now vexing problems, such as that of the spin.

The significant of the above hyperformulations of SU(3) symmetries is that of **identifying quarks as what they really are: purely mathematical objects defined on purely mathematical internal spaces without any connection with our spacetime.** In fact **u, d, s hyperquarks and their conjugates,** namely, quarks characterized by hyperunit (3.4), are regular hyperrepresentation of SU(3) that remain three-dimensional, although each dimension has 8-values.

**PROPOSED EXPERIMENT 4.1: TEST ANTIMATTER PHOTONS IN PION DECAYS.
**

*
*
Antimatter represents one of the biggest scientific unbalances of the 20-th century because matter was studied at ALL possible levels, from Newton to second quantization, while antimatter was study SOLELY at the level; of SECOND QUANTIZATION, thus leaving open fundamental open problems in the CLASSICAL treatment of antimatter, such as our inability to even initiate quantitative studies as to whether far away galaxies or quasars are made up of matter or of antimatter.

To resolve this unbalance, R. M. Santilli [3] constructed a **new mathematics,** the isodual mathematics, that permits a CLASSICAL representation of antimatter in full agreement with all classical experimental data that, after isodual quantization, results to be equivalent to charge conjugation, thus representing as well all particles experimental data on antimatter.

The latter studies predicted that **photons emitted by antimatter, called isodual photons (21), are different than those emitted by matter, and can be experimentally differentiated in a number of ways.** One of them is the **necessity for the isodual theory that antimatter, including isodual photons, experience gravitational repulsion (antigravity) in the field of matter and vice-versa** (22). Such a prediction can indeed be tested with currently available technology, such as highly sensitive interferometric technologies.

The implications for a possible experimental differentiation between photons emitted by matter and those emitted by antimatter are far reaching because, e.g., we could initiate experimental resolutions as to whether far away galaxies and quasars are made up of matter or of antimatter.**is well known in advance to be verified,** since the spectroscopy of anti-hydrogen is expected to be identical to that of the conventional hydrogen. A more FUNDAMENTAL experimental work at CERN would be the test of the NATURE (rather than the frequency) of the photons emitted by antimatter.

The studies presented in Refs. (21.22) and in this section indicate that **antimatter photons can be searched in mesons and other decays.** Consider, for instance, the proposed structure model of the p^{o}

(4.1) p^{o} = (e^^{-},e^^{+})_{hm},

According to the above model, p^{+} verifies a new fundamental symmetry, the **iso-self-duality,** (occurring when a particle-antiparticle state coincides with its antihermitean conjugate UNDER THE CONDITION OF HAVING THE SAME TOTAL ENERGY) (21,22). It then follows that the decays of the p^{o} must verify the same symmetry (see next proposed experiment for possible exceptions). The conventionally assumed decay

(4.2) p^{o} => g + g, 98.79 %

VIOLATES the iso-self-duality symmetry and, as such, it CANNOT be NECESSARILY assumed as the decay of an iso-self-dual state WITHOUT EXPERIMENTAL STUDIES. The decay predicted by the isodual theory of antimatter is given by

(4.3) p^{o} => g + g^{d},98.79 %

where g^{d} is the **isodual photon.**

Since particle accelerators can now be consider as "p^{o} factories," various experiments to ascertain possible differences between the two gs can be indeed identified and conducted via current technologies. The test here recommended is that of solely selecting (via collimators or other means) p^{o} decay gs in horizontal flight, and then testing the gravitational attraction or repulsion of the latter via sensitive interferometric equipment, or other means. Additional experiments based on isodual parity and other differences between photons and isodual photons are possible can be be outlined in more details in the eventuality of real interest by particle laboratories.

It is evident that the possible experimental verification of physical differences between photons emitted by matter and those emitted by antimatter would indeed imply a large advancement in human knowledge. However, such experimental verification would also establish a major loss by organized interests on Einsteinian doctrines and quantum mechanics (since what could amount to half of the universe would be outside both theories) and, for this reason, truly basic studies on antimatter have been carefully avoided until now, if not obstructed, jeopardized and discredited by said organized interests, as recalled in Proposed Experiment III.8.4, denounced in book (60) and documented in volumes (61). As a result, the author believes that, again, no truly fundamental test on antimatter will be possible unless there is the prior addressing of issues pertaining to scientific ethics and accountability in the current physics community.

**PROPOSED EXPERIMENT 4.2: ASCERTAIN WHETHER HADRON DECAYS VERIFY OR VIOLATE ISO-SELF-DUALITY.
**

*
*
At a first analysis it may appear that the decay

(4.4) p^{o} => e^{+} + e^{-} +
g, 1.19%,

violates iso-self-duality. However, as indicated earlier, **iso-self-duality is only applicable under the same total energy.** Also,
the p^{o} decay is based on the following processes predicted by hadronic (and NOT quantum) mechanics

(4.5a) e^^{-} => e^{-} + g

(4.5b) e^^{+} => e^{+} + g^{d},

as well as conventional electron-positron annihilation. As a result, iso-self-duality could still be verified in the event of a sufficiently large difference in kinetic energy between e^^{-} and e^^{+} such that the positron has absorbed all the energy of its isodual photon, since, positrons are predicted to experience antigravity in the field of Earth. In any case, the occurrence warrants the search for the conjugate decay

(4.6) p^{o} => e^{+} + e^{-} +
g^{d}, 1.19%,

Note that, even in the event iso-self-duality is not a universal symmetry in the particle world, decay (4.3) could still be possible.

*
*
As indicated in Section 1, the main experimental evidence used for the reduction of mesons and leptons to electrons and positrons is that of **ball lightings,** and their capability of bonding additional electrons. As well known in superconductivity and molecular chemistry, electrons bond to each other in **singlet couplings,** thus implying a **planar configuration** as that in Figure 2.

However, it is evident that ball lightings cannot be entirely composed of a very large number of electrons all in planar configuration in singlet couplings. Since ball lightings are "balls", their existence implies the capability of electrons also to bond to each other in an **axial configuration,** namely, with a coupling along their spin axes, in which case the only stable configuration is that of the triplet.

In fact, hadronic chemistry (59) predicts the existence of a bound state of electrons with spin 1, charge -2e and maximal value of the total rest energy 1.022 MeV, with its isodual,

(4.7a) E = (e^^{-},e^^{-})_{hm,J=1},

(4.7b) E^{d} = (e^^{+},e^^{+})_{hm,J=1}.

Needless to say, these states are predicted to be **unstable** and decay into two ordinary electrons and two ordinary positrons, respectively, plus possible secondary processes, although it has not been possible to predict their meanlives due to lack of experimental data.

**It should be stressed that HADRONICV QUASIPARTICLES (4.7) CAN ONLY BE PRODUCED AT THRESHOLD ENERGIES, AND ARE PREDICTED NOT TO EXIST AT ALL AT HIGH ENERGIES** (see for details Part V).

*******************************************

(4.8a) E_{J=0} = (e^^{-},e^^{-})_{hm},

(4.8b) E^{d}_{J=0} = (e^^{+},e^^{+})_{hm},

*The upper view depicts the of the triplet coupling that is necessary for the existence of ball lighting resulting in the quasiparticle*

(4.9a) E_{J=1} = (e^^{-},e^^{-})_{hm}.

(4.9b) E^{d}_{J=1} = (e^^{+},e^^{+})_{hm}.

*Note that both states (4.8) and (4.9) have the same probability because in both cases we have a Coulomb repulsion due to the equal charge, a Coulomb attraction due to opposite magnetic polarities and the same total rest energy. Despite that, the state (4.8a) is well known while state (4.9a) has been detected numerous times in particle accelerators and other processes, but its existence has been dismissed or suppressed because of academic politics surrounding Pauli's exclusion principle. In fact, state (4.8a) is compatible with Pauli's principle while state (4.9a) does not.
*

*
However, on scientific grounds outside academic politics, Pauli's principle was formulated for atomic orbits and then extended by organized academic interests to all conditions existing in the universe, although without a serious scrutiny. Once seen in this light, it is evident that, for the case of the Cooper air and molecular valence bonds, only the singlet state is possible, because we are referring to atomic orbitals for which the validity of Pauli's principle is beyond doubt. However, triplet state (4.9a) is solely predicted for nonorbital conditions, in which case the necessary validity of Pauli's exclusion principle is not established at all, and only imposed via academic pseudo-power and other nonscientific means.*

*
Differently states, when treating orbital conditions, it is evident that the only possible coupling is the planar one, in which case the only stable coupling is the singlet in full compliance with Pauli;'s principle. However, when we have electrons that DO NOT belong to atomic orbits, the very foundations for the applicability of Pauli's principle are missing, in which case all possible couplings with spins "in phase" of each others (gear model) are possible, thus yielding both configurations of this figure.
*

*
In any case, academic politics surrounding Pauli's exclusion principle is easily disqualified by the evidence that electrons in ball lighting cannot possibly all have different energies and/or be all coupled in singlet pairs, as necessary to verify the beloved Pauli's exclusion principle. It is, therefore, hoped that, one day, a real scientific process will replace current scientific religions, and issues of this basic nature are resolved one way or another via EXPERIMENTS, rather than postures of academic power.
*

*
The issue under consideration here is far from being purely academic. In fact, the existence of quasiparticle (4.9) is crucial for the reduction of all matter in the universe to protons and electrons and their antiparticles, as evident already in the structure of the kaons (Figures 6 and 7), with consequential existence of new, clean energies (see Part V). Therefore, obstructions against the experimental test of Pauli;'s principle in NON-ORBITAL conditions are true obstructions for personal equivocal gains against the search of NEW clean energies.*

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Reproduction in pdf format of the abstract, table of content and Section 5 of the original memoir (38) proposing the construction of hadronic mechanics, with the structure model of mesons and (unstable) leptons reviewed in this section:

NEED FOR SUBJECTING TO AN EXPERIMENTAL VERIFICATION THE VALIDITY WITHIN A HADRON OF EINSTEIN'S SPECIAL RELATIVITY AND PAULI¹S EXCLUSION PRINCIPLE,

Ruggero Maria Santilli,

Hadronic Journal Vol. 1, pages 574-9-2, 1978.

**6. GENERAL REFERENCES ON HADRONIC MECHANICS.
**

[1] ** HISTORICAL REFERENCES:**

(1) I. Newton, * Philosophiae Naturalis Principia Mathematica* (1687),
translated and reprinted by Cambridge Univ. Press. (1934).

(2) J. L. Lagrange, * Mechanique Analytique* (1788), reprinted by
Gauthier-Villars, Paris (1888).

(3) W. R. Hamilton, * On a General Method in Dynamics* (1834), reprinted
in {\it Hamilton's Collected Works,} Cambridge Univ. Press (1940).

(4) S. Lie, * Over en Classe Geometriske Transformationer,* English translation by E.
Trell, Algebras Groups and Geometries {\bf 15}, 395 (1998).

(5) A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. {\bf 47}, 777 (1935).

(6) P. A. M. Dirac, * The Principles of Quantum
Mechanics,* Clarendon Press, Oxford, fourth edition (1958).

(7) A. A. Albert, Trans. Amer. Math. Soc. {\bf 64}, 552 (1948).

[2] ** BASIC MATHEMATICAL PAPERS:**

(8) R. M. Santilli, Nuovo Cimento {\bf 51}, 570 (1967).

(9) R. M. Santilli, Suppl. Nuovo Cimento {\bf 6}, 1225 (l968).

(10) R. M. Santilli, Hadronic J. {\bf 3}, 440 (l979).

(11) R. M. Santilli, Hadronic J. {\bf 8}, 25 and 36 (1985).

(12) R. M. Santilli Algebras, Groups and Geometries {\bf 10}, 273 (1993).

(13) R. M. Santilli and T. Vougiouklis, contributed paper in {\it New Frontiers in
Hyperstructures,} T., Vougiouklis, Editor, Hadronic Press, p. 1 (1996).

(14) R. M. Santilli, Rendiconti Circolo Matematico di
Palermo, Supplemento {\bf 42}, 7 (1996).

(15) R. M. Santilli, Intern. J. Modern Phys. D {\bf 7}, 351 (1998).

[3] ** ISODUAL FORMULATIONS:**

(16) R. M. Santilli, Comm. Theor. Phys. {\bf 3}, 153 (1993).

(17) R. M. Santilli, Hadronic J. {\bf 17}, 257 (1994).

(18) R. M. Santilli, Hadronic J. {\bf 17}, 285 (1994).

(19) R. M. Santilli, Communication of the JINR, Dubna, Russia,. No. E2-96-259 (1996).

(20) R. M. Santilli, contributed paper in {\it New Frontiers of Hadronic Mechanics,}
T.L.Gill, ed., Hadronic Press (1996).

(21) R. M. Santilli, Hyperfine Interactions, {\bf 109}, 63 (1997).

(22) R. M. Santilli, Intern. J. Modern Phys. A {\bf 14}, 2205 (1999).

[4] ** ISOTOPIC FORMULATIONS:**

(23) R.M.Santilli: Hadronic J. {\bf 1}, 224 (1978).

(24) R. M. Santilli, Phys. Rev. D {\bf 20}, 555 (1979).

(25) C.Myung and R.M.Santilli, Hadronic J. {\bf 5}, 1277 (1982).

(26) R. M. Santilli, Novo Cimento Lett. {\bf 37}, 545 (1983).

(27) R. M. Santilli, Hadronic J. {\bf 8}, 25 and 36 (1985).

(28) R. M. Santilli, JINR Rapid. Comm. {\bf 6}, 24 (1993).

(29) R. M. Santilli, J.Moscow Phys.Soc. {\bf 3}, 255 (1993).

(30) R. M. Santilli, Chinese J.Syst.Ing. \& Electr.{\bf 6}, 177 (1996).

(31) R. M. Santilli, Found. Phys. {\bf 27}, 635 (1997).

(32) R. M. Santilli, Found. Phys. Letters {\bf 10}, 307 (1997).

(33) R. M. Santilli, Acta Appl. Math. {\bf 50}, 177 (1998).

(34) R. M. Santilli, contributed paper to the {\it Proceedings of the International Workshop on
Modern Modified Theories of Gravitation and Cosmology,} E. I. Guendelman, Editor, Hadronic Press, p. 113 (1998).

(35) R. M. Santilli, contributed paper to the {\it Proceedings of the VIII M. Grossmann Meeting
on General Relativity,} Jerusalem, June 1998, World Scientific, p. 473 (1999).

(36) R. M. Santilli, contributed paper in {\it Photons: Old Problems in Light of New Ideas,} V. V.
Dvoeglazov, editor, Nova Science Publishers, pages 421-442 (2000).

(37) R. M. Santilli, Found. Phys. Letters {\32}, 1111 (2002).

[5] ** GENOTOPIC FORMULATIONS:**

(38) R. M. Santilli: Hadronic J. {\bf 1},574 and 1267 (1978).

(39) R. M. Santilli, Hadronic J. {\bf 2}, 1460 (l979) and {\bf 3}, 914 (l980).

(40) R. M. Santilli, Hadronic J. {\bf 4}, 1166 (l981).

(41) R. M. Santilli, Hadronic J. {\bf 5}, 264 (l982).

(42) H. C. Myung and R. M. Santilli, Hadronic J. {\bf 5}, 1367 (l982).

(43) R. M. Santilli, Hadronic J. Suppl. {\bf 1}, 662 (l985).

(44) R. M. Santilli, Found. Phys. {\bf 27}, 1159 (1997).

(45) R. M. Santilli, Modern Phys. Letters {\bf 13}, 327 (1998).

(46) R. M. Santilli, Intern. J. Modern Phys. A {\bf 14}, 3157 (1999).

[6] ** HYPERSTRUCTURAL FORMULATIONS:**

(47) R. M. Santilli, Algebras, Groups and Geometries {\bf 15}, 473 (1998).

[7] ** MONOGRAPHS:**

(48) R. M. Santilli, {\it Foundations of Theoretical Mechanics}, Vol. I,
Springer--Verlag, Heidelberg--New York (1978).

(49) R. M. Santilli, {\it Lie-admissible Approach to the Hadronic Structure,}
Vol.I, Hadronic Press, Palm Harbor, Florida (1978).

(50) R. M. Santilli, {\it Lie-admissible Approach to the Hadronic Structure,} Vol.
II, Hadronic Press, Palm Harbor, Florida (1981).

(51) R. M. Santilli, {\it Foundations of Theoretical Mechanics}, Vol. II,
Springer--Verlag, Heidelberg--New York (1983).

(52) R. M. Santilli, {\it Isotopic Generalizations of Galilei and Einstein Relativities,}
Vol. I, Hadronic Press, Palm Harbor, Florida (1991).

(53) R. M. Santilli, {\it Isotopic Generalizations of Galilei and Einstein Relativities,}
Vol. II, Hadronic Press, Palm Harbor, Florida (1991).

(54) R. M. Santilli, {\it Elements of Hadronic Mechanics},
Vol I, Ukraine Academy of Sciences,
Kiev, Second Edition (1995).

(55) R. M. Santilli, {\it Elements of Hadronic Mechanics},
Vol II, Ukraine Academy of Sciences,
Kiev, Second Edition (1995).

(56) C. R. Illert and R. M. Santilli, {\it Foundations of Theoretical Conchology,}
Hadronic Press, Palm Harbor, Florida (1995).

(57) R. M. Santilli {\it Isotopic, Genotopic and Hyperstructural Methods
in Theoretical Biology}, Ukraine Academy of Sciences, Kiev (1996).

(58) R. M. Santilli, {\it The Physics of New Clean Energies and Fuels According to
Hadronic Mechanics,} Special issue of the Journal of New Energy, 318 pages (1998).

(59) R. M. Santilli, {\it Foundations of Hadronic Chemistry with Applications to New
Clean Energies and Fuels,} Kluwer Academic Publishers, Boston-Dordrecht-London
(2001).

(60) R. M. Santilli, {\it Ethical Probe of Einstein's Followers in the USA: An insider's view,} Alpha Publishing, Newtonville, MA (1984).

(61) R. M. Santilli, {\it Documentation of the Ethical Probe,} Volumes I, II and III, Alpha Publishing, Newtonville, MA (1985).

(62) H. C. Myung, {\it Lie Algebras and Flexible
Lie-Admissible Algebras,} Hadronic Press (1982).

(63) A.K. Aringazin, A. Jannussis, D.F. Lopez, M. Nishioka, and B. Veljanoski,
{\it Santilli's Lie-isotopic Generalization of Galilei's and Einstein's
Relativities,} Kostarakis Publishers, Athens (1991).

(64) D. S. Sourlas and G. T. Tsagas, {\it Mathematical
Foundations of the Lie-Santilli Theory,} Ukraine Academy of Sciences,
Kiev (1993).

(65) J. L\^{o}hmus, E. Paal and L. Sorgsepp, {\it
Nonassociative Algebras in Physics}, Hadronic Press, Palm Harbor, FL,
USA (1994).

(66) J. V. Kadeisvili, {\it Santilli's Isotopies of
Contemporary Algebras, Geometries and Relativities},
Second Edition, Ukraine Academy of Sciences, Kiev , Second Edition (1997).

(67) R. M. Falcon Ganfornina and J. Nunez Valdes, {\it Fondamentos de la Isoteoria de
Lie-Santilli,} (in Spanish) International Academic Press, America-Europe-Asia,
(2001), also available in the pdf file
http://www.i-b-r.org/docs/spanish.pdf

(68) Chun-Xuan Jiang, {\it Foundations of Santilli's Isonumber Theory,}
with Applications to New Cryptograms, Fermat's Theorem and Goldbach's Conjecture,
International Academic Press, America-Europe-Asia
(2002) also available in the pdf file
http://www.i-b-r.org/docs/jiang.pdf

[8] ** CONFERENCE PROCEEDINGS AND REPRINT VOLUMES:**

(69) H. C. Myung and S. Okubo, Editors, {\it Applications of Lie-Admissible Algebras
in Physics,} Volume I, Hadronic Press (1978).

(70) H. C. Myung and S. Okubo, Editors, {\it Applications of Lie-Admissible Algebras
in Physics,} Vol. II, Hadronic Press (1978).

(71) H. C. Myung and R. M. Santilli, Editor, {\it Proceedings of the Second Workshop on
Lie-Admissible Formulations,} Part I, Hadronic J. Vol. 2, no. 6, pp. 1252-2033 (l979).

(72) H. C. Myung and R. M. Santilli, Editor, {\it Proceedings of the Second Workshop on
Lie-Admissible Formulations,}Part II, Hadronic J. Vol. 3, no. 1, pp. 1-725 (l980.

(73) H. C. Myung and R. M. Santilli, Editor, {\it Proceedings of the Third Workshop on
Lie-Admissible Formulations,}Part A, Hadronic J. Vol. 4, issue no. 2, pp. 183-607 (l9881).

(74) H. C. Myung and R. M. Santilli, Editor, {\it Proceedings of the Third Workshop on
Lie-Admissible Formulations,} Part B, Hadronic J. Vo. 4, issue no. 3, pp. 608-1165 (l981).

(75) H. C. Myung and R. M. Santilli, Editor, {\it Proceedings of the Third Workshop on
Lie-Admissible Formulations,} Part C, Hadronic J. Vol. 4, issue no. 4, pp. 1166-1625
(l981).

(76) J. Fronteau, A. Tellez-Arenas and R. M. Santilli, Editor, {\it Proceedings of the First
International Conference on Nonpotential Interactions and their Lie-Admissible
Treatment,} Part A, Hadronic J., Vol. 5, issue no. 2, pp. 245-678 (l982).

(77) J. Fronteau, A. Tellez-Arenas and R. M. Santilli, Editor, {\it Proceedings of the First
International Conference on Nonpotential Interactions and their Lie-Admissible
Treatment,} Part B, Hadronic J. Vol. 5, issue no. 3, pp. 679-1193 (l982).

(78) J. Fronteau, A. Tellez-Arenas and R. M. Santilli, Editor, {\it Proceedings of the First
International Conference on Nonpotential Interactions and their Lie-Admissible
Treatment,} Part C, Hadronic J. Vol. 5, issue no. 4, pp. 1194-1626 (l982).

(79) J. Fronteau, A. Tellez-Arenas and R. M. Santilli, Editor, {\it Proceedings of the First
International Conference on Nonpotential Interactions and their Lie-Admissible
Treatment,} Part D, Hadronic J. Vol. 5, issue no. 5, pp. 1627-1948 (l982).

(80) J.Fronteau, R.Mignani, H.C.Myung and R. M. Santilli, Editors, {\it Proceedings of the
First Workshop on Hadronic Mechanics,} Hadronic J. Vol. 6, issue no. 6, pp. 1400-1989
(l983).

(81) A. Shoeber, Editor, {\it Irreversibility and Nonpotentiality in Statistical Mechanics,}
Hadronic Press (1984).

(82) H. C. Myung, Editor, {\it Mathematical Studies in Lie-Admissible Algebras,} Volume I,
Hadronic Press (1984).

(83) H. C. Myung, Editor, {\it Mathematical Studies in Lie-Admissible Algebras,} Volume II,
Hadronic Press (1984).

(84) H. C. Myung and R. M. Santilli, Editor, {\it Applications of Lie-Admissible Algebras
in Physics,} Vol. III, Hadronic Press (1984).

(85) J.Fronteau, R.Mignani and H.C.Myung, Editors, {\it Proceedings of the Second Workshop on
Hadronic Mechanics,} Volume I Hadronic J. Vol. 7, issue no. 5, pp. 911-1258 (l984).

(86) J.Fronteau, R.Mignani and H.C.Myung, Editors, {\it Proceedings of the Second Workshop on
Hadronic Mechanics,} Volume II, Hadronic J. Vol. 7, issue no. 6, pp. 1259-1759 (l984).

(87) D.M.Norris et al, {\it Tomber's Bibliography and Index in Nonassociative
Algebras,} Hadronic Press, Palm Harbor, FL (1984).

(88) H. C. Myung, Editor, {\it Mathematical Studies in Lie-Admissible Algebras,} Volume III,
Hadronic Press (1986).

(89) A.D.Jannussis, R.Mignani, M. Mijatovic, H. C.Myung B. Popov and A. Tellez Arenas,
Editors, {\it Fourth Workshop on Hadronic Mechanics and Nonpotential Interactions,}
Nova Science, New York (l990).

(90) H. M. Srivastava and Th. M. Rassias, Editors, {\it Analysis Geometry and Groups:
A Riemann Legacy Volume,} Hadronic Press (1993).

(91) F. Selleri, Editor, {\it Fundamental Questions in Quantum Physics and Relativity,}
Hadronic Press (1993).

(92) J. V. Kadeisvili, Editor, {\it The Mathematical Legacy of Hanno Rund}, Hadronic Press
(1994).

(93) M. Barone and F. Selleri Editors, {\it Frontiers of Fundamental Physics,} Plenum, New
York, (1994).

(94) M. Barone and F. Selleri, Editors, {\it Advances in Fundamental Physics,} Hadronic Press
(1995).

(95) Gr. Tsagas, Editor, {\it New Frontiers in Algebras, Groups and Geometries
,} Hadronic Press (1996).

(96) T. Vougiouklis, Editor, {\it New Frontiers in Hyperstructures,}
Hadronic Press, (1996).

(97) T. L. Gill, Editor, {\it New Frontiers in Hadronic Mechanics,} Hadronic Press (1996).

(98) T. L. Gill, Editor, {\it New Frontiers in Relativities,} Hadronic Press (1996).

(99) T. L. Gill, Editor, {\it New Frontiers in Physics,}, Volume I, Hadronic Press (1996).

(100) T. L. Gill, Editor, {\it New Frontiers in Physics,}, Volume II, Hadronic Press (1996).

(101) C. A. Dreismann, Editor, {\it New Frontiers in Theoretical Biology,} Hadronic Press
(1996).

(102) G. A., Sardanashvily, Editor,{\it New Frontiers in Gravitation,} Hadronic Press (1996).

(103) M. Holzscheiter, Editor, {\it Proceedings of the
International Workshop on Antimatter Gravity,} Sepino, Molise, Italy,
May 1996, Hyperfine Interactions, Vol. {\bf 109} (1997).

(104) T. Gill, K. Liu and E. Trell, Editors, {\it Fundamental Open Problems in Science at the
end of the Millennium,}} Volume I, Hadronic Press (1999).

(105) T. Gill, K. Liu and E. Trell, Editors, {\it Fundamental Open Problems in Science at the
end of the Millennium,}} Volume II, Hadronic Press (1999).

(106) T. Gill, K. Liu and E. Trell, Editors, {\it Fundamental Open Problems in Science at the
end of the Millennium,}} Volume III, Hadronic Press (1999).

(107) V. V. Dvoeglazov, Editor {\it Photon: Old Problems in Light of New Ideas,} Nova Science
(2000).

(108) M. C. Duffy and M. Wegener, Editors, {\it Recent Advances in Relativity Theory} Vol. I,
Hadronic Press (2000).

(109) M. C. Duffy and M. Wegener, Editors, {\it Recent Advances in Relativity Theory} Vol. I,
Hadronic Press (2000).

[9] ** EXPERIMENTAL VERIFICATIONS:**

(110) F. Cardone, R. Mignani and R. M. Santilli, J. Phys. G: Nucl. Part. Phys.
{\bf 18}, L61 (1992).

(111) F. Cardone, R. Mignani and R. M. Santilli, J. Phys. G: Nucl. Part. Phys. {\bf 18}, L141
(1992).

(112) R. M. Santilli, Hadronic J. {\bf 15}, Part I: 1-50 and Part II: 77134 (l992).

(113) Cardone and R. Mignani, JETP {\bf 88}, 435 (1995).

(114) R. M. Santilli, Intern. J. of Phys. {\bf 4}, 1 (1998).

(115) R. M. Santilli Communications in Math. and Theor. Phys. {\bf 2}, 1 (1999).

(116) A. O. E. Animalu and R. M. Santilli, Intern. J. Quantum Chem. {\bf 26},175 (1995).

(117) R. M. Santilli, contributed paper to {\it Frontiers of Fundamental Physics,} M. Barone and
F. Selleri, Editors Plenum, New York, pp 4158 (1994).

(118) R. Mignani, Physics Essays {\bf 5}, 531 (1992).

(119) R. M. Santilli, Comm. Theor. Phys. {\bf 4}, 123 (1995).

(120) Yu. Arestov, V. Solovianov and R. M. Santilli, Found. Phys. Letters {\bf 11}, 483 (1998).

(121) R. M. Santilli, contributed paper in the {\it Proceedings of the International Symposium on
Large Scale Collective Motion of Atomic Nuclei,} G. Giardina, G. Fazio and M. Lattuada,
Editors, World Scientific, Singapore, p. 549 (1997).

(122) J.Ellis, N.E. Mavromatos and D.V.Napoulos in {\sl Proceedings of the
Erice Summer School, 31st Course: From Superstrings to the Origin of Space--Time},
World Sientific (1996).

(123) C. Borghi, C. Giori and A. Dall'OIlio Russian J. Nucl. Phys. {\bf 56}, 147 (1993).

(124) N. F. Tsagas, A. Mystakidis, G. Bakos, and L. Seftelis, Hadronic J. {\bf 19}, 87 (1996).

(125) R. M. Santilli and D., D. Shillady, Intern. J. Hydrogen Energy {\bf 24}, 943 (1999).

(126) R. M. Santilli and D., D. Shillady, Intern. J. Hydrogen Energy {\bf 25}, 173 (2000).

(127) R. M. Santilli, Hadronic J. {\bf 21}, pages 789-894 (1998).

(128) M.G. Kucherenko and A.K. Aringazin, Hadronic J. {\bf 21}, 895 (1998).

(129) M.G. Kucherenko and A.K. Aringazin, Hadronic Journal {\bf 23}, 59 (2000).

(130) R.M. Santilli and A.K. Aringazin, "Structure and Combustion of
Magnegases", e-print http://arxiv.org/abs/physics/0112066, to be published.

,
[10] ** MATHEMATICS PAPERS:**

(131) S. Okubo, Hadronic J. {\bf 5}, 1564 (1982).

(132) J. V. Kadeisvili, Algebras, Groups and Geometries {\bf 9}, 283 and 319 (1992).

(133) J. V. Kadeisvili, N. Kamiya, and R. M. Santilli, Hadronic J. {\bf 16}, 168 (1993).

(134) J. V. Kadeisvili, Algebras, Groups and Geometries {\bf 9}, 283 (1992).

(135) J. V. Kadeisvili, Algebras, Groups and Geometries {\bf 9}, 319 (1992).

(136) J. V. Kadeisvili, contributed paper in the {\it Proceedings of the
International Workshop on Symmetry Methods in Physics,} G. Pogosyan et al., Editors,
JINR, Dubna, Russia (1994).

(137) J. V. Kadeisvili, Math. Methods in Appl. Sci. {\bf 19} 1349 (1996).

(138) J. V. Kadeisvili, Algebras, Groups and Geometries, {\bf 15}, 497 (1998).

(139) G. T. Tsagas and D. S. Sourlas, Algebras, Groups and Geometries {\bf 12}, 1 (1995).

(140) G. T. Tsagas and D. S. Sourlas, Algebras, Groups and geometries {\bf 12}, 67 (1995).

(141) G. T. Tsagas, Algebras, Groups and geometries {\bf 13}, 129 (1996).

(142) G. T. Tsagas, Algebras, Groups and geometries {\bf 13}, 149 (1996).

(143) E. Trell, Isotopic Proof and Reproof of Fermat¹s Last Theorem Verifying Beal¹s
Conjecture. Algebras Groups and Geometries {\bf 15}, 299-318 (1998).

(144) A.K. Aringazin and D.A. Kirukhin,, Algebras, Groups and
Geometries {\bf 12}, 255 (1995).

(145) A.K. Aringazin, A. Jannussis, D.F. Lopez, M. Nishioka, and B. Veljanoski, Algebras, Groups and Geometries {\bf 7}, 211 (1990).

(146) A.K. Aringazin, A. Jannussis, D.F. Lopez, M.
Nishioka, and B. Veljanoski, Algebras, Groups and
Geometries {\bf 8}, 77 (1991).

(147) D. L. Rapoport, Algebras, Groups and Geometries, {\bf 8}, 1 (1991).

(148) D. L. Rapoport, contributed paper in the{\it
Proceedings of the Fifth International Workshop on
Hadronic Mechanics,} H.C. Myung, Edfitor, Nova Science Publisher (1990).

(149) D. L. Rapoport, Algebras, Groups and Geometries {\bf 8}, 1 (1991).

(150) C.-X. Jiang, Algebras, Groups and Geometries {\bf 15}, 509 (1998).

(151) D. B. Lin, Hadronic J. {\bf 11}, 81 (1988).

(152) R. Aslaner and S. Keles, Algebras, Groups and Geometries {\bf 14}, 211 (1997).

(153) R. Aslander and S. Keles,. Algebras, Groups and Geometries {\bf 15}, 545 (1998).

(154) M. R. Molaei, Algebras, Groups and Geometries {\bf 115}, 563 (1998) (154).

(155) S. Vacaru, Algebras, Groups and Geometries {\bf 14}, 225 (1997) (155).

(156) N. Kamiya and R. M. Santilli, Algebras, Groups and Geometries {\bf 13}, 283 (1996).

(157) S. Vacaru, Algebras, Groups and Geometries {\bf 14}, 211 (1997).

(158) Y. Ylamed, Hadronic J. {\bf 5}, 1734 (1982).

(159) R. Trostel, Hadronic J. {\bf 5}, 1893 (1982).

[11] **PHYSICS PAPERS:**

(160) J. P. Mills, jr, Hadronic J. {\bf 19}, 1 (1996).

(161) J. Dunning-Davies, Foundations of Physics Letters, {\bf 12}, 593 (1999).

(162) E. Trell, Hadronic Journal Supplement {\bf 12}, 217 (1998).

(163) E. Trell, Algebras Groups and Geometries {\bf 15}, 447-471 (1998).

(164) E. Trell, "Tessellation of
Diophantine Equation Block Universe," contributed paper to {\it Physical
Interpretations of Relativity Theory,} 6-9 September 2002, Imperial College, London.
British Society for the Philosophy of Science, in print, (2002).

(165) J. Fronteau, R. M. Santilli and A. Tellez-Arenas, Hadronic J. {\bf 3}, 130 (l979).

(166) A. O. E. Animalu, Hadronic J.{\bf 7}, 19664 (1982).

(167) A. O. E. Animalu, Hadronic J. {\bf 9}, 61 (1986).

(168) A. O. E. Animalu, Hadronic J. {\bf 10}, 321 (1988).

(169) A. O. E. Animalu, Hadronic J. {\bf 16}, 411 (1993).

(170) A. O. E. Animalu, Hadronic J. {\bf 17}, 349 (1994).

(171) S.Okubo, Hadronic J. {\bf 5}, 1667 (1982).

(172) D.F.Lopez, in {\it
Symmetry Methods in Physics}, A.N.Sissakian, G.S.Pogosyan and X.I.Vinitsky, Editors (
JINR, Dubna, Russia (1994).

(173) D. F. Lopez, {\it Hadronic J.} {\bf 16}, 429 (1993).

(174) A.Jannussis and D.Skaltsas,{\it Ann. Fond. L.de Broglie} {\bf
18},137 (1993).

(175) A.Jannussis, R.Mignani and R.M.Santilli,
{\it Ann.Fonnd. L.de Broglie} {\bf 18}, 371 (1993).

(176) A. O. Animalu and R. M. Santilli, contributed paper in {\it Hadronic
Mechanics and Nonpotential Interactions} M. Mijatovic, Editor,
Nova Science, New York, pp. 19-26 (l990).

(177) M. Gasperini, Hadronic J. {\bf 6}, 935 (1983).

(178) M. Gasperini, Hadronic J. {\bf 6}, 1462 (1983).

(179) R. Mignani, Hadronic J. {\bf 5}, 1120 (1982).

(180) R. Mignani, Lett. Nuovo Cimento {\bf 39}, 413 (1984).

(181) A. Jannussis, Hadronic J. Suppl. {\bf 1}, 576 (1985).

(182) A. Jannussis and R. Mignani, Physica A {\bf 152}, 469 (1988).

(183) A. Jannussis and I.Tsohantis, Hadronic J. {\bf 11}, 1 (1988).

(184) A. Jannussis, M. Miatovic and B. Veljanosky, Physics Essays {\bf 4}, (1991).

(185) A. Jannussis, D. Brodimas and R. Mignani, J. Phys. A: Math. Gen. {\bf 24}, L775 (1991).

(186) A. Jannussis and R. Mignani, Physica A {\bf 187}, 575 (1992).

(187) A.Jannussis, R.Mignani and D.Skaltsas Physics A {\bf 187}, 575 (1992).

(188) A.Jannussis et al, Nuovo Cimento B{\bf 103}, 17 and 537 (1989).

(189) A. Jannussis et al., Nuovo Cimento B{\bf 104}, 33 and 53 (1989).

(190) A. Jannussis et al. Nuovo Cimento B{\bf 108} 57 (l993).

(191) A. Jannussis et al., Phys. Lett. A {\bf 132}, 324 (1988).

(192) A.K. Aringazin, Hadronic J. {\bf 12}, 71 (1989).

(193) A.K. Aringazin, Hadronic J. {\bf13}, 183 (1990).

(194) A.K. Aringazin, Hadronic J. {\bf 13}, 263 (1990).

(195) A.K. Aringazin, Hadronic J. {\bf 14}, 531 (1991).

(196) A.K. Aringazin, Hadronic J. {\bf 16}, 195 (1993).

(197) A.K. Aringazin and K.M. Aringazin,Invited paper, in the {\it Proceedings of the Intern.
Conference 'Frontiers of Fundamental Physics',} Plenum Press, (1993).

(198) A.K. Aringazin, K.M. Aringazin, S. Baskoutas, G. Brodimas, A. Jannussis, and K. Vlachos,
contribuuted paper in the {\it Proceedings of the Intern. Conference 'Frontiers of Fundamental
Physics',} Plenum Press, (1993).

(199) A.K. Aringazin, D.A. Kirukhin, and R.M. Santilli, Hadronic J. {\bf 18}, 245 (1995).

(200) A.K. Aringazin, D.A.Kirukhin, and R.M. Santilli, Had-ronic J. {\bf 18}, 257 (1995).

(201) T. L. Gill, Hadronic J. {\bf 9}, 77 (1986).

(202) T. L. Gill and J. Lindesay, Int. J. Theor,
Phys {\bf} 32}, 2087 (1993).

(203) T. L. Gill, W.W. Zachary, M.F. Mahmood and J. Lindesay,
Hadronic J. {\bf 16}, 28 (1994).

(204) T.L. Gill, W.W. Zachary and J. Lindesay,
Foundations of Physics Letters {\bf 10}, 547 (1997).

(205) T.L. Gill, W.W. Zachary and J.
Lindesay, Int. J. Theo Phys {\bf 37}, 22637 (1998).

(206) T.L. Gill, W.W. Zachary and J.
Lindesay, Foundations of Physics, {\bf 31}, 1299 (2001).

(207) D. L. Schuch, K.-M. Chung and H. Hartmann,
J. Math. Phys. {\bf 24}, 1652 (1983).

(208) D. L. Schuch and K.-M. Chung, Intern. J. Quantum
Chem. {\bf 19}, 1561 (1986).

(209) D. Schich 23, Phys. Rev. A {\bf 23}, 59, (1989).

(210) D. Schuch, contributed paper in {\it New
Frontiers in Theoretical Physics,} Vol. I, p 113, T. Gill Editor, Hadronic Press, Palm Harbor
(1996); D. L. Schuch, Hadronic J. {\bf 19}, 505 (1996).

(211) S.L. Adler, Phys.Rev. {\bf 17}, 3212 (1978).

(212) Cl.George, F. Henin, F.Mayene and I.Prigogine, Hadronic J. {\bf 1},
520 (1978).

(213) C.N.Ktorides, H.C.Myung and R.M.Santilli, Phys. Rev. D {\bf 22}, 892
(1980).

(214) R. M. Santilli, Hadronic J. {\bf 13}, 513 (1990).

(215) R. M. Santilli, Hadronic J. {\bf 17}, 311 (1994).

(216) A.J. Kalnay, Hadronic J. {\bf 6}, 1 (1983).

(217) A. J. Kalnay and R. M. Santilli, Hadronic J. {\bf 6}, 1873 (1983).

(218) M. 0. Nishioka, Nuovo Cimento A {\bf 82}, 351 (1984).

(219) G.Eder, Hadronic J. \underline{\bf 4,} (1981) and {\bf 5}, 750 (1982).

(220) H. E. Wilhelm, contributed paper in {\it
Space, Time and Motion: Theory and Experiments}, H., E. Wilhelm and K. Liu, editors,Chinese J.
Syst Eng. Electr., {\bf 6}, issue 4 (1995).

(221) C.A.Chatzidimitriou-Dreismann, T. Abdul-Redah, R.M.F. Streffer, J.Mayers
Phys. Rev. Lett. {\bf 79}, 2839 (1997).

(222) C.A.Chatzidimitriou-Dreismann, T. Abdul-Redah, B. Kolaric
J. Am. Chem. Soc. {\bf 123}, 11945 (2001).

(223) C.A.Chatzidimitriou-Dreismann, T. Abdul-Redah,
R.M.F. Streffer, J.Mayers J. Chem.
Phys. {\bf 116}, 1511 (2002) (see also
www.ISIS.rl.ac.uk/molecularspectroscopy/EVS).

(224) R. M. Santilli, Hadronic J. Suppl. {\bf 1}, 662 (l985).

(225) R. M. Santilli, Found. Phys. {\bf 11}, 383 (l981).

(226) R. M. Santilli, "Iso-m geno-, hyper-mechanifor matter and their isoduals for antimatter," in press at *Journal of Dynamical Systems and Geometric Theories,* also available in pdf format.

(227) R. M. Santiulli, Comm. Thgeor. Phys. {\bf 4} 123 (1995).

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(237) V. V. Burov et al., JINR Communication E4-95-440 (1995), Dubna, Russia.

(238) R. M. Santilli, in *Proceedings of "Deuteron 1993",* JINR, Dubna, Russia (1994).

(239) R. M. Santilli, Intern. J. Hydrogen Energy {\bf 28}, 177 (2003).

(240) A. Enders and G.
Nimtz, J. Phys. France {\bf 2}, 1693 (1992).

(241) G. Nimtz and W. Heitmann,
Progr. Quantum Electr. {\bf 21}, 81 (1997).

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(243) J. Tingay et al., Nature {\bf {374}}, 141 (1995).

(244) D. Baylin et al., IAU Comm. 6173 (1995).

(246) P. Saari and K. Reivelt, Phys. Rev. Letters {\bf 79} (1997), in press.

(247) E. Recami and R. M. Santilli, Hadronic Journal {\bf 23}, 279 (2000).

(248) H. Arp, * Quasars Redshifts and Controversies,* Interstellar media, Berkeley, 1987.

(249) H. Arp, contributed paper in * Frontiers of Fundamental Physics, F. Selleri and M. Barone, Editors, Editors, Plenum, New York (1994).
*

*
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*

*
(252) R. M. Santilli, Hadronic J. Suppl. 4A, issues 1 (252a), 2 (244b), 3 (252c) and 4 (252d), 1988.
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(253) R. M. Santilli, contributed paper in Frontiers of Fundamental Physics, F. Selleri and M. Barone, Editors, Editors, Plenum, New York (1994).*

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(254) P. Marmet, IEEE Trans. Plasma Sci. {\bf 17}, 238 (1988)
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