[27] **viXra:1305.0202 [pdf]**
*replaced on 2014-08-03 19:19:59*

**Authors:** Nathan O. Schmidt

**Comments:** 34 pages, 6 figures, accepted in the Hadronic Journal

We propose a preliminary algorithm which is designed to reduce aspects of the n-body problem to a 2-body problem for holographic principle compliance. The objective is to share an alternative view-point on the n-body problem to try and generate a simpler solution in the future. The algorithm operates 2D and 3D data structures to initiate the encoding of the chaotic dynamical system equipped with modified superfluid order parameter fields in both 3D and 4D versions of the Inopin holographic ring (IHR) topology. For the algorithm, we arbitrarily select one point-mass to be the origin and, from that reference frame, we subsequently engage a series of instructions to consolidate the residual (n-1)-bodies to the IHR. Through a step-by-step example, we demonstrate that the algorithm yields "IHR effective" (IHRE) net quantities that enable us to hypothetically define an IHRE potential, kinetic, and Lagrangian.

**Category:** Mathematical Physics

[26] **viXra:1305.0201 [pdf]**
*replaced on 2014-07-28 05:49:23*

**Authors:** Leonardo Pedro

**Comments:** 14 Pages. Propostion 7.2 corrected

There are Poincare group representations on complex Hilbert spaces, like the Dirac
spinor field, or real Hilbert spaces, like the electromagnetic field tensor. The Majorana
spinor is an element of a 4 dimensional real vector space. The Majorana spinor field is a
space-time dependent Majorana spinor, solution of the free Dirac equation.
The Majorana-Fourier and Majorana-Hankel transforms of Majorana spinor fields are
defined and related to the linear and angular momenta of a spin one-half representation of
the Poincare group. We show that the Majorana spinor field with finite mass is an unitary
irreducible projective representation of the Poincare group on a real Hilbert space.
Since the Bargmann-Wigner equations are valid for all spins and are based on the free
Dirac equation, these results open the possibility to study Poincare group representations
with arbitrary spins on real Hilbert spaces.

**Category:** Mathematical Physics

[25] **viXra:1305.0173 [pdf]**
*submitted on 2013-05-29 00:07:18*

**Authors:** John Frederick Sweeney

**Comments:** 5 Pages. Copyright John Frederick Sweeney 2013

Qi Men Dun Jia is an ancient form of divination from China which is still employed to make accurate predictions, and thus meets the definition of a scientific model based on scientific theory. This paper introduces a series of books which engages in "reverse engineering," using the concepts of contemporary mathematical physics to explain how this ancient model works. Specifically, we address Clifford Algebras, Bott Periodicity, Exceptional Lie Algebras, icosians, octonions and sedenions, as well as the Fano Plane and isometric relationships to Leptons and Baryons. The introduction concludes with reference to extremely ancient and superior science from 12,000 years ago, ancient Vedic culture and extremely ancient Egyptian culture.

**Category:** Mathematical Physics

[24] **viXra:1305.0171 [pdf]**
*replaced on 2013-07-25 15:35:48*

**Authors:** Jose javier garcia Moreta

**Comments:** 19 Pages.

•ABSTRACT: We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals for positive ‘s’ , using the Euler Maclaurin summation formula, we manage to express a divergent integral in term of a linear combination of divergent series , these series can be regularized using the Riemann Zeta function s >0 , in the case of the pole at s=1 we use a property of the Functional determinant to obtain the regularization , with the aid of the Laurent series in one and several variables we can extend zeta regularization to the cases of integrals , we believe this method can be of interest in the regularization of the divergent UV integrals in Quantum Field theory since our method would not have the problems of the Analytic regularization or dimensional regularization

**Category:** Mathematical Physics

[23] **viXra:1305.0145 [pdf]**
*submitted on 2013-05-23 10:52:34*

**Authors:** Branko Zivlak

**Comments:** 5 Pages. 1 Table, 1 Appendix

This article is about relations between fundamental physical constants. The mass, radius and cycle of the universe are the basis for calculating Planck units.

**Category:** Mathematical Physics

[22] **viXra:1305.0137 [pdf]**
*submitted on 2013-05-22 22:25:06*

**Authors:** Jian-zhong Zhao

**Comments:** 14 Pages.

Zanaboni Theory is mathematically analyzed in this paper. The conclusion is that Zanaboni Theorem is invalid and not a proof of Saint-Venant's Principle; Discrete Zanaboni Theorem and Zanaboni's energy decay are inconsistent with Saint-Venant's decay; the inconsistency, discussed here, between Zanaboni Theory and Saint-Venant's Principle provides more proofs that Saint-Venant's Principle is not generally true.

**Category:** Mathematical Physics

[21] **viXra:1305.0136 [pdf]**
*submitted on 2013-05-22 22:34:09*

**Authors:** Jian-zhong Zhao

**Comments:** 8 Pages.

The problem of statement of Saint-Venant's Principle is concerned. Statement of Boussinesq or Love is ambiguous so that its interpretations are in contradiction with each other. Rationalized Statement of Saint-Venant’s Principle of elasticity is suggested to rule out the ambiguity of Statements of Boussinesq and Love. Rational Saint-Venant's Principle is suggested to fit and guide applications of the principle to fields of continuum physics and cover the analogical case as well as the non-analogical case discovered and discussed in this paper . `` Constraint-free " problems are suggested and `` Constraint-free " Rational Saint-Venant's Principle or Rational Saint-Venant's Principle with Relaxed Boundary Condition is developed to generalize the principle and promote its applications to fields of continuum physics . Applications of Analogical Rational Saint-Venant's Principle and `` Constraint-free " Rational Saint-Venant's Principle are exemplified, emphasizing `` properness " of the boundary-value problems. Three kinds of properly posed boundary-value problems, i.e., the boundary-value problem with the undetermined boundary function, the boundary-value problem with the implicit boundary condition and the boundary-value problem with the explicit boundary condition, are suggested for both `` constrained " and `` constraint-free " problems.

**Category:** Mathematical Physics

[20] **viXra:1305.0132 [pdf]**
*submitted on 2013-05-21 05:51:06*

**Authors:** Dan Visser

**Comments:** 6 Pages.

This article is about a new formula for dark energy force. This has already been published in a series of my articles in the archive vixra, but gets little attention. The new formula is part of a larger universe than the Big Bang, called the Double Torus hypothesis. The new dark energy force is different from dark energy in the Big Bang, because it uses the extension of time. This article emphases the extra time relating gravity and a new topology of quantum-spin of point particles, such as electrons. This article describes that cohesion by my dark energy force formula in a Double Torus Universe.

**Category:** Mathematical Physics

[19] **viXra:1305.0124 [pdf]**
*submitted on 2013-05-19 07:49:32*

**Authors:** Andrew Beckwith

**Comments:** 4 Pages. 1st of six posters for the ICM 2 conference in Prague.

The following questions are raised in this document. First, can@@ there be a stable (massive) graviton? If so, does this massive graviton, as modeled by KK DM, with a modification of slight 4 dimensional space mass, contribute to DE, at least in terms of re acceleration ? The answer, if one assumes that the square of a frequency for graviton mass is real valued and greater than zero appears to be affirmative. The author, when considering a joint DM – DE model finds evidence that re acceleration of the universe one billion years ago in a higher dimensional setting can be justified in terms of a slight modification of standard KK DM models, if one considers how an information exchange between present to prior universes occurs, which the author thinks mandates more than four dimensional space time geometry

**Category:** Mathematical Physics

[18] **viXra:1305.0123 [pdf]**
*submitted on 2013-05-19 07:52:54*

**Authors:** Andrew Beckwith

**Comments:** 4 Pages. Poster or virtual paper for the ICM 2 conference

This paper uses the “Fjortoft theorem” for defining necessary conditions for instability. The point is that it does not apply in the vicinity of the big bang. We apply this theorem to what is called by T. Padmanabhan a thermodynamic potential which becomes would be unstable if conditions for the applications of “Fjortoft’s theorem” hold. In our case, there is no instability, so a different mechanism has to be appealed to. In the case of vacuum nucleation, we argue that conditions exist for the nucleation of particles as of the electroweak regime. Due to injecting material from a node point, in spacetime. This regime of early universe creation, coexits with the failure of applications of “Fjortoft” theorem in such a way as to give necessary and sufficient conditions for matter creation, in a way similar to the Higgs Boson

**Category:** Mathematical Physics

[17] **viXra:1305.0122 [pdf]**
*submitted on 2013-05-19 07:54:46*

**Authors:** Andrew Beckwith

**Comments:** 4 Pages.

When initial radius R approaches zero if we use Stoica actually derived Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. The implications of the initial radius approaching zero are the first part of this manuscript. Then the resolution is alluded to by work from Muller and Lousto, as to entanglement entropy implications of entanglement entropy. We present entanglement entropy in the early universe with a steadily shrinking scale factor, due to work from Muller and Lousto , and show that there are consequences due to initial entanged entropy for a time dependent horizon radius in cosmology, with for flat space conditions r(H)=conformal time. In the case of a curved, but not flat space version of entropy, we look at vacuum energy as proportional to the inverse of scale factor squared times the inverse of initial entropy, effectively when there is no initial time except with in line with the conformal time being almost zero. . The consequences for this initial entropy being entangled are elaborated in this manuscript. No matter how small the initial radial length gets, then for initial cosmological entropy if it is entanglement entropy, initial cosmological entropy will not go to zero.

**Category:** Mathematical Physics

[16] **viXra:1305.0121 [pdf]**
*submitted on 2013-05-19 07:56:51*

**Authors:** Andrew Beckwith

**Comments:** 4 Pages.

First, we show through a numerical simulation that the massive Schwinger model used to formulate solutions to CDW transport is insufficient for transport of solitons (anti-solitons) through a pinning gap model of CDW transport. We show that a model Hamiltonian with Peierls condensation energy used to couple adjacent chains (or transverse wave vectors) permits formation of solitons (anti- solitons) which could be used to transport CDW through a potential barrier. We argue that there are analogies between this construction and the false vacuum hypothesis used for showing a necessary and sufficient condition for formation of CDW soliton – anti - soliton (S-S’) pairs in wave functionals presented in a prior publication

**Category:** Mathematical Physics

[15] **viXra:1305.0120 [pdf]**
*submitted on 2013-05-19 07:58:57*

**Authors:** Andrew Beckwith

**Comments:** 4 Pages.

The author asks if octonion quantum gravity is relevant near the Planck scale. Furthermore, the question is raised if gravitational waves would be generated during the initial phase, , of the universe when an increase in degrees of freedom have in setting , so that the result can be observed by a gravitational detector.. The well appreciated .quantum gravity problem that the notion of a quantum state, representing the structure of spacetime at some instant, and the notion of the evolution of the state, does not get traction, since there are no real “instants”, is avoided by having the initial octonion geometry embedded in a larger, non linear “pilot model” (semi classical) embedding structure. The Penrose suggestion of re cycled space time avoiding a ‘big crunch’ is picked as the embedding structure, so as to avoid the ‘instants’ of time issue. In addition the favored idea is to avoid the well known string theory trap known as the dimensionality problem of an equation of motion (consistency condition) which is the reason why string theory dimensionality is either (10 or 26) depending upon if super symmetry is imposed. Getting octonion gravity as embedded in a larger, Pilot theory embedding structure may restore Quantum Gravity to its rightful place in early cosmology without the lunacy of then afterwards ‘Schrodinger equation ‘ states of the universe, forevermore afterwards. Setting , in a GW detector due to appropriate measurement procedures may allow the opportunity to find experimental clues as to this embedding structure in which octonion gravity may emerge in the Planckian regime.of evolutionary cosmology

**Category:** Mathematical Physics

[14] **viXra:1305.0118 [pdf]**
*submitted on 2013-05-19 08:00:58*

**Authors:** Andrew Beckwith

**Comments:** 4 Pages.

The following questions is asked, If one takes the covariant derivative of a Stress-energy representation of early universe massive gravitons, is the derivative of the Graviton stress tensor equal to zero ? If so, then in what range of astrophysics does this occur, and when does this formalism break down? Lavenda and Davies argued that the derivative of a generalized GR stress energy tensor being zero in itself is insufficient to show that the 1st law of thermodynamics alone holds. If the full Stress-Energy tensor expression for GR is written out, there is a stress energy tensor component involving GW alone which we highlight. The problem as to this test is if the derivative of the Stress energy tensor, for gravitons as written by Visser is brought up. This Visser stress energy tensor for massive gravitons will not even satisfy the 1st thermodynamic law. We bring this up as a counter point to an article written by Lavenda and Davies purporting to claim that the Tolman test for a first law of thermodynamics which they generalize to first and second law of thermodynamics for inflationary cosmology. We show a breakdown of a zero value for the derivative of the Stress energy tensor for early universe massive gravitons and this derivative of the massive Graviton Stress energy tensor (Visser) will not even satisfy the first law of thermodynamics according to the Tolman criteria. Note that if the Visser Massive Graviton Stress energy tensor scenario does not hold then the Lavenda and Davies objection to inflation is upheld.

**Category:** Mathematical Physics

[13] **viXra:1305.0100 [pdf]**
*submitted on 2013-05-17 03:47:11*

**Authors:** Maurizio M. D'Eliseo

**Comments:** 13 Pages.

Orbital averages are employed to compute the secular variation of the elliptical planetary elements
in the orbital plane in presence of perturbing forces of various kinds. They are also useful as an
aid in the computation of certain complex integrals. An extensive list of computed integrals is given.

**Category:** Mathematical Physics

[12] **viXra:1305.0099 [pdf]**
*submitted on 2013-05-16 08:37:03*

**Authors:** Richard L. Amoroso, Elizabeth A. Rauscher

**Comments:** 6 Pages.

We have analyzed, calculated and extended the modification of Maxwell’s equations in a complex Minkowski metric, M4 in a C2 space using the SU2 gauge, SL(2,c) and other gauge groups, such as SUn for n >2 expanding the U1 gauge theories of Weyl. This work yields additional predictions beyond the electroweak unification scheme. Some of these are: 1) modified gauge invariant conditions, 2) short range non-Abelian force terms and Abelian long range force terms in Maxwell’s equations, 3) finite but small rest of the photon, and 4) a magnetic monopole like term and 5) longitudinal as well as transverse magnetic and electromagnetic field components in a complex Minkowski metric M4 in a C4 space.

**Category:** Mathematical Physics

[11] **viXra:1305.0085 [pdf]**
*replaced on 2013-08-09 16:17:16*

**Authors:** Nathan O. Schmidt

**Comments:** 30 pages, 2 figures, published in the Hadronic Journal

In this work, we forge a powerful, easy-to-visualize, flexible, consistent, and disciplined abstract vector framework for particle and astro physics that is compliant with the holographic principle. We demonstrate that the structural properties of the complex number and the sphere enable us to introduce and define the triplex number---an influential information structure that is similar to the 3D hyper-complex number by D. White and P. Nylander---which identifies a 3D analogue of (2D) complex space. Consequently, we engage the complex and triplex numbers as abstract vectors to systematically encode the state space of the Riemannian dual 3D and 4D space-time topologies, where space and time are dual and interconnected; we use the triplex numbers (with triplex multiplication) to extend 1D and 2D algebraic systems to 3D and 4D configurations. In doing so, we equip space-time with order parameter fields for topological deformations. Finally, to exemplify our motivation, we provide three example applications for this framework.

**Category:** Mathematical Physics

[10] **viXra:1305.0071 [pdf]**
*submitted on 2013-05-12 06:33:07*

**Authors:** Dan Visser

**Comments:** 2 Pages.

The Higgs-particle could be a dark matter particle! It is not enough to confirm spin 0 and + parity for the Higgs-like particle to let it be the Higgs-particle. The Double Torus hypothesis should be involved. A dark matter particle in this new framework could also have spin 0 and + parity under condition it contributes to gravity, but its properties can also contribute as negative mass to anti-gravity.

**Category:** Mathematical Physics

[9] **viXra:1305.0056 [pdf]**
*submitted on 2013-05-08 15:06:47*

**Authors:** Richard L. Amoroso, Elizabeth A. Rauscher

**Comments:** 19 Pages.

We develop a formalism for the Schrödinger equation in an eight
dimensional complex Minkowski space and discuss its relation to the Dirac equation,
properties of nonlocality, remote connectedness, Young’s double slit experiment, Bell’s
Theorem, the EPR paradox and anticipatory parameters of spacetime; and also identify
an imaginary temporal component as a small nonlinear term and find soliton or solitary
wave solutions. These coherent solutions can carry information over long distances, are
consistent with Lorentz invariance and appear to provide a fundamental methodology
for describing the issue of quantum measurement and a new context for the basis of
quantum theory. In the Copenhagen view models of reality are not desirable. However
our new approach may enable the redefinition of concepts of reality from a new
nonlocal anticipatory quantum theory. Certainly the most desirable consequence of
scientific discovery is the ability to redefine our concepts of reality.

**Category:** Mathematical Physics

[8] **viXra:1305.0055 [pdf]**
*submitted on 2013-05-08 15:09:12*

**Authors:** Richard L. Amoroso, Elizabeth A. Rauscher

**Comments:** 25 Pages.

Many naturally occurring phenomena require theoretical treatment
utilizing complex analysis by methods such as the Cauchy-Riemann relations using
hyper-geometrical spaces which treat inherently nonlinear, non-dispersive,
collective nonlocal resonant states of a quantum system, so as to be consistent with
the nonlinearity inherent in General Relativity. Typical quantum approaches form
linear approximations limiting the ability to formulate a quantum consistent
Relativity Theory.

**Category:** Mathematical Physics

[7] **viXra:1305.0049 [pdf]**
*submitted on 2013-05-08 06:04:29*

**Authors:** Andrej Rehak

**Comments:** 4 Pages.

Geometric demonstration of free fall and rotation reveals space-time nature of the genesis of circle. We show that the operations with radius are equivalent to operations with velocity. Consequently, conventional spatial unit for radius (m), becomes equivalent to dynamic space-time unit for speed (m/s). We prove that the velocity is a physical equivalence of geometric idea of radius.

**Category:** Mathematical Physics

[6] **viXra:1305.0048 [pdf]**
*submitted on 2013-05-08 06:10:03*

**Authors:** Andrej Rehak

**Comments:** 8 Pages.

Geometric demonstration located in v, t diagram explains the nature of the period of a pendulum, i.e. the universal connection of time with velocity (radius) and acceleration. Conceptual nature of the principles proof points to its universal validity. In other words, if it is valid for a circle, it is valid. Through the geometry of free fall we describe physical nature of irrational numbers π and √2. We demonstrate physical matrix of scale √2nπ. Through the relationship between the variables of space, time and velocity, using the principle of the pendulum, we illustrate the foundation of the law of conservation of energy. Analyzing its motion we point to nature of distortion of Euclidean geometry.

**Category:** Mathematical Physics

[5] **viXra:1305.0033 [pdf]**
*submitted on 2013-05-05 00:05:04*

**Authors:** Temur Z. Kalanov

**Comments:** 8 Pages.

Critical analysis of the generally accepted (standard) foundations of differential and integral calculus is proposed. Methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is shown that the generally accepted foundations are based on the logically and practically erroneous concepts “infinitesimal quantity (uninterruptedly diminishing quantity)”, “derivative”, “derivative as function of variable quantity” and, consequently, represent incorrect basis of mathematics and of theoretical physics.

**Category:** Mathematical Physics

[4] **viXra:1305.0032 [pdf]**
*submitted on 2013-05-05 00:09:30*

**Authors:** Temur Z. Kalanov

**Comments:** 10 Pages.

The critical analysis of the Pythagorean theorem and of the problem of irrational numbers is proposed. Methodological basis for the analysis is the unity of formal logic and of rational dialectics. It is shown that: 1) the Pythagorean theorem represents a conventional (conditional) theoretical proposition because, in some cases, the theorem contradicts the formal-logical laws and leads to the appearance of irrational numbers; 2) the standard theoretical proposition on the existence of incommensurable segments is a mathematical fiction, a consequence of violation of the two formal-logical laws: the law of identity of geometrical forms and the law of lack of contradiction of geometrical forms; 3) the concept of irrational numbers is the result of violation of the dialectical unity of the qualitative aspect (i.e. form) and quantitative aspect (i.e. content: length, area) of geometric objects. Irrational numbers represent a calculation process and, therefore, do not exist on the number scale. There are only rational numbers.

**Category:** Mathematical Physics

[3] **viXra:1305.0031 [pdf]**
*submitted on 2013-05-05 00:13:38*

**Authors:** Temur Z. Kalanov

**Comments:** 11 Pages.

The work is devoted to solution of an actual problem – the problem of relation between geometry and natural sciences. Methodological basis of the method of attack is the unity of formal logic and of rational dialectics. It is shown within the framework of this basis that geometry represents field of natural sciences. Definitions of the basic concepts "point", "line", "straight line", "surface", "plane surface", and “triangle” of the elementary (Euclidean) geometry are formulated. The natural-scientific proof of the parallel axiom (Euclid’s fifth postulate), classification of triangles on the basis of a qualitative (essential) sign, and also material interpretation of Euclid’s, Lobachevski’s, and Riemann’s geometries are proposed.

**Category:** Mathematical Physics

[2] **viXra:1305.0010 [pdf]**
*submitted on 2013-05-01 19:19:35*

**Authors:** R.L. Amoroso, L.H. Kauffman, E.A. Rauscher, P. Rowlands J-P Vigier

**Comments:** 27 Pages.

Recent attempts to consider isolated particles and real constitutive wave elements as localized,
extended spacetime structures (i.e., moving within time-like hypertubes or branes are developed within a causal
extension of the Feynman-Gell-Mann electron model. These extended structures contain real internal motions,
(i.e., internal hidden parameters) locally correlated with the "hidden parameters" describing the local collective
motions of the corresponding pilot-waves. Recent experimental evidence is briefly discussed.

**Category:** Mathematical Physics

[1] **viXra:1305.0009 [pdf]**
*submitted on 2013-05-01 19:35:02*

**Authors:** Richard L. Amoroso, Elizabeth A. Rauscher

**Comments:** 18 Pages.

Here we present discussion for the utility of resonant interference in Calabi-Yau mirror symmetry as a
putative empirical test of the existence of virtual tachyon / tardon interactions in a covariant Dirac polarized vacuum

**Category:** Mathematical Physics