Mathematical Physics

Previous months:
2007 - 0703(2)
2008 - 0812(1)
2009 - 0907(1) - 0908(3) - 0909(1) - 0910(2)
2010 - 1001(3) - 1002(1) - 1003(1) - 1006(13) - 1007(2) - 1009(2) - 1010(3) - 1011(1) - 1012(5)
2011 - 1101(4) - 1102(4) - 1103(3) - 1104(1) - 1105(3) - 1106(2) - 1107(2) - 1108(4) - 1109(2) - 1110(1) - 1111(10) - 1112(2)
2012 - 1201(3) - 1202(2) - 1203(6) - 1204(3) - 1205(5) - 1206(8) - 1207(4) - 1208(4) - 1209(2) - 1210(2) - 1211(4) - 1212(7)
2013 - 1301(8) - 1302(7) - 1303(7) - 1304(5) - 1305(27) - 1306(5) - 1307(8) - 1308(7) - 1309(7) - 1310(9) - 1311(12) - 1312(2)
2014 - 1401(10) - 1402(8) - 1403(16) - 1404(11) - 1405(8) - 1406(6) - 1407(4) - 1408(9) - 1409(7) - 1410(6) - 1411(7) - 1412(8)
2015 - 1501(11) - 1502(10) - 1503(9) - 1504(10) - 1505(12) - 1506(9) - 1507(8) - 1508(9) - 1509(4) - 1510(19) - 1511(11) - 1512(8)
2016 - 1601(5) - 1602(8) - 1603(8) - 1604(6) - 1605(14) - 1606(11) - 1607(5) - 1608(13) - 1609(17) - 1610(17) - 1611(6) - 1612(23)
2017 - 1701(9) - 1702(9) - 1703(5) - 1704(10) - 1705(17) - 1706(9) - 1707(14) - 1708(14) - 1709(6) - 1710(16) - 1711(11) - 1712(7)
2018 - 1801(16) - 1802(19) - 1803(9) - 1804(10) - 1805(6) - 1806(8) - 1807(6) - 1808(14) - 1809(11) - 1810(13) - 1811(7) - 1812(4)
2019 - 1901(10) - 1902(9) - 1903(6) - 1904(15) - 1905(5) - 1906(10) - 1907(6) - 1908(11)

Recent submissions

Any replacements are listed farther down

[888] viXra:1908.0483 [pdf] submitted on 2019-08-23 10:16:21

On the Polchinski’s Equation Concerning the Exact Renormalization Group. Mathematical Connections with Some Sectors of Ramanujan Mathematics, String Theory and Particle Physics

Authors: Michele Nardelli, Antonio Nardelli
Comments: 144 Pages.

In the present research thesis, we have obtained various and interesting new possible mathematical connections concerning the exact renormalization group and some sectors of Ramanujan mathematics, String Theory and Particle Physics
Category: Mathematical Physics

[887] viXra:1908.0479 [pdf] submitted on 2019-08-24 01:14:12

On the Nature of Maxwell and Dirac Field

Authors: Vu B Ho
Comments: 16 Pages.

In this work we discuss the nature of Maxwell and Dirac field by examining the mathematical structures of the subfields that are coupled to form these two physical fields. We show that while Maxwell and Dirac field are hyperbolic fields which are described by wave equations the subfields are elliptic fields which are described by elliptic equations. Therefore, it is reasonable to suggest that the subfields are more fundamental and should be used to represent quantum particles in stable states with invariant physical properties. Furthermore, since the subfields are described by elliptic equations therefore they comply with the Euclidean relativity rather than the pseudo-Euclidean relativity as Maxwell and Dirac fields do, and this results in profound implications such as if quantum particles possess physical properties that are represented by subfields which are described by elliptic equations, hence acting in accordance with the Euclidean relativity, then they can be used to explain physical phenomena that require physical transmissions with speeds greater than the speed of light in vacuum, such as the Einstein-Podosky-Rosen paradox in quantum entanglement. As a further discussion, we also show that it is possible to formulate a Dirac-like elliptic field that complies with the Euclidean relativity.
Category: Mathematical Physics

[886] viXra:1908.0431 [pdf] submitted on 2019-08-20 07:41:02

On the New Developments Concerning the Mock Theta Functions of Various Order. Further Mathematical Connections with Some Sectors of Particle Physics and Black Hole Physics.

Authors: Michele Nardelli, Antonio Nardelli
Comments: 161 Pages.

In the present research thesis, we have obtained further interesting mathematical connections with various Ramanujan’s Mock theta functions of order 8, order 7, order 6, order 2 and some sectors of Particle Physics and Black Hole Physics.
Category: Mathematical Physics

[885] viXra:1908.0329 [pdf] submitted on 2019-08-15 19:28:24

Not Theory

Authors: Bheemaiah, Anil Kumar
Comments: 3 Pages.

Abstract: Not theory is a derivation from standard Knot Theory, inspired by Knots and topological spaces in the E8 theory of Unification. In Not Theory, we consider an E8 based fiber theory of nature, extending it to a simulated universe as strands. Not theory is about the mathematics of the application of ‘nots’ to strands. In this paper, we consider a closure proof, and proof of completeness to not applications on arbitrary not as applicable to a particle and quasi-particle model. What: Axioms: A strand is a fundamental resonance of nature starting in one singularity and ending in another. These two singularities are in E8 space-time, with many operators acting on them. Axiom: Any quasi-particle or particle can be described as an aspect of a strand, a resonance in space-time. Theorem 1: Closure: Operation of a not on a strand leads to a resonance in energy time of space and momentum which is also a strand. Theorem 2: Completeness: All particle and quasi-particle interactions can be represented as strands.
Category: Mathematical Physics

[884] viXra:1908.0299 [pdf] submitted on 2019-08-15 01:44:10

On the Ramanujan’s Mock Theta Functions of Tenth Order: New Possible Mathematical Developments and Mathematical Connections with Some Sectors of Particle Physics and Black Hole Physics II

Authors: Michele Nardelli, Antonio Nardelli
Comments: 136 Pages.

In the present research thesis, we have obtained various and interesting new possible mathematical developments concerning some Ramanujan’s Mock theta functions of tenth order and Mathematical connections with some sectors of Particle Physics and Black Hole physics
Category: Mathematical Physics

[883] viXra:1908.0286 [pdf] submitted on 2019-08-15 14:58:34

A New Approach to Proof the Riemann Hypothesis Using New Operator

Authors: Rafik Zeraoulia
Comments: 09 Pages. no comments

In this note we present a new approach to proof the Riemann hypothesis one of the most important open problem in pure mathematics using a new operator derived from unitary operator groups acts on Riemann-Siegal function and it uses partition function for Hamiltonian operator , The interest idea is to compute the compositional inverse of Riemann zeta function at $s=-\frac12$ such as we show that:$\zeta^{-1}(-\frac12) =\zeta(\frac12+i \beta)=0$ for some $\beta >0 $
Category: Mathematical Physics

[882] viXra:1908.0162 [pdf] submitted on 2019-08-09 18:38:30

Do Radial Velocities of Given Bodies Mean Zero-Equivalent Time?

Authors: M.V Nembahe
Comments: 4 Pages.

There's a general consensus among cosmologists; that the zero-equivalent time (t=0) can only mean the present (now) as far as the Hubble constant is concerned. But the constant's initial value of 0 is problematic; as it misuses distance and time in conjunction with the Cartesian coordinate system and together I find have nothing to do with the quantification of t=0 and so run the risk of predicting infinitesimal velocity of infinite distance and time.
Category: Mathematical Physics

[881] viXra:1908.0154 [pdf] submitted on 2019-08-10 05:19:34

On Various Equations Inherent the Works Concerning JT Gravity, Open Strings on the Rindler Horizon, Gauge Theory and Integrability and Topological Gravity. New Mathematical Connections with Some Sectors of Ramanujan’s Mathematics.

Authors: Michele Nardelli, Antonio Nardelli
Comments: 357 Pages. UPDATED VERSION

In this research paper we have obtained some interesting mathematical connections between various equations inherent the works concerning JT Gravity, open strings on the Rindler Horizon, Gauge Theory and integrability and Topological Gravity of Witten et al. and some sectors of Ramanujan’s mathematics, principally the Mock Theta Functions and ζ(2) and some expressions concerning the mass of some particles.
Category: Mathematical Physics

[880] viXra:1908.0138 [pdf] submitted on 2019-08-07 10:57:53

Riemann Hypothesis Through the Glance of Infinite Quantum System

Authors: Germann Frosch
Comments: 2 Pages.

In this article we briefly show how to connect Riemann Hypothesis to the Infinite Quantum System. We obtain the needed results. Simple example of such quantum system is a Frog sound system.
Category: Mathematical Physics

[879] viXra:1908.0116 [pdf] submitted on 2019-08-08 03:07:47

The Proof of the Riemann Hypothesis

Authors: Heinz Volkenborn
Comments: 1 page

The proof of the Riemann Hypothesis requires a decoding of the fine-structure constant in which is shown, why the Riemann zeta function cannot show a zero point with Re (s) = 1, off the critical line Re (s) = 1/2
Category: Mathematical Physics

[878] viXra:1908.0033 [pdf] submitted on 2019-08-03 01:43:34

Ramanujan Approximations to π, Invariant Class and Other Expressions: Further Mathematical Connections with Some Sectors of Particle Physics, String Theory and Physics of Black Holes (Entropy)

Authors: Michele Nardelli, Antonio Nardelli
Comments: 172 Pages.

In this research paper, we have obtained further mathematical connections with some sectors of Particle Physics, String Theory and Physics of Black Holes (entropy) and the Ramanujan approximation to π, invariant class and other expressions extracted from some pages of original manuscript
Category: Mathematical Physics

[877] viXra:1907.0525 [pdf] submitted on 2019-07-26 12:34:20

A Theory of Second Order Linear Variable Coefficient Equations

Authors: Ayéna Vignon Régis Yehossou, Marcellin Nonti, Jean Akande, Marc Delphin Monsia
Comments: 2 pages

A class of second order linear variable differential equations which may exhibit elementary function solutions is developed in this paper. It is shown that this class includes as special case the equation record in Kamke’s book as equation 2. 80.
Category: Mathematical Physics

[876] viXra:1907.0398 [pdf] submitted on 2019-07-22 02:32:07

Energy-Momentum is not Defined Globally, But Locally

Authors: Dmitri Martila
Comments: 11 Pages. Manuscript is copyrighted by Estonian Notar Agency.

Slow precession of the Earth rotation axis, and the Moon-Earth orbital resonance were accompanied during centuries by Newton's and Laplace's explanations. However, in the present paper, the author considers the possibility of additional factor: the small violation of the global energy-momentum conservation. Thus, the energy-momentum concept being not conserved, cannot be regarded as total (global) energy-momentum of system. The recently experimentally verified Lense-Thirring Effect and the Mercury's perihelion anomalous shift cannot be found in Newton Physics, and the latter demands the global energy-momentum conservation. Thus, the shift violates global energy-momentum conservation. Why? Because the energy-momentum is defined locally, not globally.
Category: Mathematical Physics

[875] viXra:1907.0365 [pdf] submitted on 2019-07-18 08:11:09

On the Possible Mathematical Connections Between Some Equations of the ‘Black Hole Entropy and Soft Hair’, Black Hole Physics, Ramanujan’s Class Invariants and Mock Theta Functions

Authors: Michele Nardelli, Antonio Nardelli
Comments: 202 Pages.

In the present research thesis, we have obtained various and interesting mathematical connections between some equations of the ‘Black Hole Entropy and Soft Hair’, the fundamental last paper of S.W. Hawking, mathematics and physics of Black Hole, Ramanujan’s Class Invariants and Mock Theta Functions
Category: Mathematical Physics

[874] viXra:1907.0180 [pdf] submitted on 2019-07-12 08:20:03

On Some Ramanujan Formulas: New Possible Mathematical Developments and Mathematical Connections with the Mass Value of Candidate “glueball” F0(1710) Meson, Other Particles and the Black Hole Entropies.

Authors: Michele Nardelli, Antonio Nardelli
Comments: 150 Pages.

In the present research thesis, we have obtained various and interesting new possible mathematical results concerning various Ramanujan’s formulas. Furthermore, we have described new possible mathematical connections with the mass value of candidate “glueball” f0(1710) meson, other particles and with the Black Hole entropies.
Category: Mathematical Physics

[873] viXra:1907.0104 [pdf] submitted on 2019-07-06 15:01:54

On Some Formulas Concerning the Ramanujan’s Master Theorem: New Possible Mathematical Developments and Mathematical Connections with the Mass Value of Candidate “glueball” F0(1710) Meson, Dark Photons and the Black Hole Entropies.

Authors: Michele Nardelli, Antonio Nardelli
Comments: 181 Pages.

In the present research thesis, we have obtained various and interesting new possible mathematical results concerning some equations of the Ramanujan’s Master Theorem. Furthermore, we have described new possible mathematical connections with the mass value of candidate “glueball” f0(1710) meson, Dark Photons and with the Black Hole entropies.
Category: Mathematical Physics

[872] viXra:1907.0027 [pdf] submitted on 2019-07-01 07:41:08

On the Ramanujan’s Mock Theta Functions of Tenth Order: New Possible Mathematical Developments and Mathematical Connections with Some Sectors of Particle Physics and Black Hole Physics I

Authors: Michele Nardelli, Antonio Nardelli
Comments: 185 Pages.

In the present research thesis, we have obtained various and interesting new possible mathematical developments concerning some Ramanujan’s Mock theta functions of tenth order and mathematical connections with some sectors of Particle Physics and Black Hole physics
Category: Mathematical Physics

[871] viXra:1906.0468 [pdf] submitted on 2019-06-24 10:38:02

The Physical Interpretation of Gravity Constants , Electron and Photons

Authors: Markos Georgallides
Comments: 121 Pages.

Article 81 is engaged with the Physical Interpretation of Gravity and Gravitational constants , the Origin of Hydrogen cave , Electron and Photon . The Analysis of Work which is Motion , or Energy is in priority .The Quantiation of Geometry and Energy results to the Material Geometry which was prior analyzed . A discussion on all referred Subjects follows with a mathematical analysis on every referred subject . A criticism is done on EPR Argument and is presented a current method to what is a Physical Quantity in cosmos .The Growth Golden ratio Pattern is analytically shown and also the How Electromagnetic issues and works everywhere in nature from the microcosm to the macrocosm
Category: Mathematical Physics

[870] viXra:1906.0382 [pdf] submitted on 2019-06-21 15:30:26

On the Ramanujan’s Mock ϑ-Functions of His Last Letter: Mathematical Connections with Some Expressions Concerning the Mass of Some Particles, the Black Hole Entropy and the Hypothetical Mass of Dark Matter Particles. II

Authors: Michele Nardelli, Antonio Nardelli
Comments: 234 Pages.

In this research paper we have obtained some interesting mathematical connections between the Mock Theta functions of the Ramanujan’s last letter and some expressions concerning the mass of some particles, the black hole entropy and the hypothetical mass of Dark Matter particles
Category: Mathematical Physics

[869] viXra:1906.0253 [pdf] submitted on 2019-06-15 02:09:19

On the Ramanujan’s Mock ϑ-Functions of His Last Letter: Mathematical Connections with Some Sectors of Particle Physics, Cosmology, Some Expressions Concerning Monster Group, Black Hole Entropies and Hypothetical Mass of Dark Matter Particles.

Authors: Michele Nardelli, Antonio Nardelli
Comments: 220 Pages.

In this research paper we have obtained some interesting mathematical connections between the Mock Theta functions of the Ramanujan’s last letter and some sectors of Particle Physics, Cosmology and some expressions concerning the Monster Group, the Black Hole entropies and the hypothetical mass of Dark Matter particles
Category: Mathematical Physics

[868] viXra:1906.0239 [pdf] submitted on 2019-06-13 13:20:47

A Mathematical Expression for Inverse Fine-Structure Constant

Authors: Alan Michael Gómez Calderón
Comments: 2 Pages.

From the golden angle to the Pell constant, a simple, elegant and concise mathematical expression of the inverse fine-structure constant is given.
Category: Mathematical Physics

[867] viXra:1906.0214 [pdf] submitted on 2019-06-12 12:48:22

Exact Periodic Solutions of Truly Nonlinear Oscillator Equations and Quadratic Liénard-Type Equations

Authors: Y. J. F. Kpomahou, L. H. Koudahoun, K. K. D. Adjaï, J. Akande, M. D. Monsia
Comments: 16 pages

The present research contribution is devoted to solving the integrability problem of Liénard type differential equations. It is shown that such a problem may be solved by nonlocal transformation for some classes of equations. By doing so, it is observed that the integrability of a class of restricted Duffing type equations with integral power or fractional power nonlinearity may be secured by that of a general class of quadratic Liénard type differential equation, and vice versa. Such a restricted Duffing type equation is also shown to be closely related to a quadratic Liénard type equation for which exact and explicit general solution may be computed. In this context it has been shown that exact and general periodic solutions may be computed for these two classes of restricted Duffing equations and quadratic Liénard type equations. The comparison of obtained solutions with some well-known results is carried out in some cases.
Category: Mathematical Physics

[866] viXra:1906.0213 [pdf] submitted on 2019-06-12 12:54:39

Descriptions of Elementary Particles plus Dark Matter plus Dark Energy and Explanations for Some Related Data

Authors: Thomas J. Buckholtz
Comments: 33 pages

We suggest united models and specific predictions regarding elementary particles, dark matter, aspects of galaxy evolution, dark energy, and aspects of the cosmology timeline. Results include specific predictions for new elementary particles and specific descriptions of dark matter and dark energy. Some of our modeling matches known elementary particles and extrapolates to predict other elementary particles, including bases for dark matter. Some modeling explains observed ratios of effects of dark matter to effects of ordinary matter. Some models suggest aspects of galaxy formation and evolution. Some modeling correlates with eras of increases or decreases in the observed rate of expansion of the universe. Our modeling framework features mathematics for isotropic quantum harmonic oscillators and provides a framework for creating physics theories. Some aspects of our approach emphasize existence of elementary particles and de-emphasize motion. Some of our models complement traditional quantum field theory and, for example, traditional calculations of anomalous magnetic dipole moments.
Category: Mathematical Physics

[865] viXra:1906.0212 [pdf] submitted on 2019-06-12 13:00:31

Integrability Analysis of a Generalized Truly Nonlinear Oscillator Equation

Authors: L. H. Koudahoun, Y. J. F. Kpomahou, J. Akande, K. K. D. Adjaï, M. D. Monsia
Comments: 6 pages

The integrability of a general class of Liénard type equations is investigated through equation transformation theory. In this way it is shown that such a class of Liénard equations can generate a generalization of some interesting truly nonlinear oscillator equations like the cube and fifth root differential equations. It has then become possible to compute the exact and general solution to the generalized truly nonlinear oscillator equation. Under an appropriate choice of initial conditions, exact and explicit solution has been obtained in terms of Jacobi elliptic functions.
Category: Mathematical Physics

[864] viXra:1906.0093 [pdf] submitted on 2019-06-08 05:09:59

Cosmos Without Big Bang

Authors: Dan Visser
Comments: 6 Pages.

I summarize my new theory for the universe in a nutshell. We are a variable hologram in a Rotating Torus Hologram Universe (RTHU). The moment I began to think the Big Bang did not exist, the universe has changed already. That was in 2004, 5 years before I started to write my articles in 2009. The main issue since then is: There is no darkness. Events happen everywhere, but rather in the RTHU than in the Postmodern Big Bang Universe (PBBU). According to all of my theoretical results a lot of events, however, remain temporarily invisible due to being shifted in the variable hologram-universe. The main cause thereto is, that a dark matter force, marked as duo-bits, is the engine of the hologram-rotation, while being located below the Planck-boundary. Hence this deeper area must be a part of a universe, the RTHU. A new parameter Tdan is the hologram-dynamic parameter and in size equivalent to the RTHU as well as in size equivalent as a building-stone of the RTHU. In that sense an under laying information is variable-divided but continuously in order to remain all the information that shapes the RTHU. Furthermore I refer to practical evidence-issues. Study my recent articles.
Category: Mathematical Physics

[863] viXra:1906.0054 [pdf] submitted on 2019-06-04 09:15:19

The Fermionic Quantum Plane

Authors: Antoine Balan
Comments: 1 page, written in english

Here is defined the fermionic quantum plane and the fermionic quantum group of transformations of it.
Category: Mathematical Physics

[862] viXra:1906.0038 [pdf] submitted on 2019-06-03 06:12:39

On the Possible Mathematical Connections Between Various Ramanujan’s Equations and Some Sectors of Particle Physics, String Theory and Physics of Black Holes

Authors: Michele Nardelli, Antonio Nardelli
Comments: 172 Pages.

In this research paper, we have described and analyzed the possible mathematical connections between various Ramanujan’s equations and some sectors of Particle Physics (rest mass of meson f0(1710), mass of proton, electric charge of positron, mass of Higgs boson), String Theory and Physics of Black Holes (entropy)
Category: Mathematical Physics

[861] viXra:1905.0616 [pdf] submitted on 2019-05-31 05:50:12

A Geometric and Topological Quantisation of Mass

Authors: Vu B Ho
Comments: 9 Pages.

In this work we discuss a geometric and topological quantisation of mass by extending our work on the principle of least action in which the quantisation of both the angular momentum of a Bohr hydrogen atom and the charge of an elementary particle can be shown to be quantised from the continuous deformation of a differentiable manifold. Similar to the case of the quantisation of charge using the two-dimensional Ricci scalar curvature, we show that in the case of three-dimensional differentiable manifolds we can apply the Yamabe problem, which states that any Riemannian metric on a compact smooth manifold of dimension greater or equal to three is conformal to a metric with constant scalar curvature, to show that mass can also be quantised by the deformation of differentiable manifolds. The Yamabe problem is a generalisation of the uniformisation theorem for two-dimensional differentiable manifolds. We also discuss whether quantum particles can be expressed as direct sums of quantum masses when they possess mathematical structures of differentiable manifolds, with the quantum masses are considered as prime manifolds. This may be regarded as a physical manifestation of an established mathematical proposition in differential geometry and topology that states that any compact, connected, and orientable differentiable manifold M can be decomposed into prime manifolds and the decomposition is unique up to an absorption or emission of 3-spheres S^3. This process of decomposition of differentiable manifolds into prime manifolds and the radiation of 3-spheres is similar to the radiation of the quanta of physical fields from a quantum system, such as the radiation of photons from a hydrogen atom. Even though our work is highly speculative and suggestive, we hope that it may pay way for further rigorous mathematical investigations into whether mass is also quantised like charge and other fundamental entities in physics.
Category: Mathematical Physics

[860] viXra:1905.0587 [pdf] submitted on 2019-05-29 07:46:52

On the Various Mathematical Connections with the Ramanujan’s Numbers 1729, 728, the Ramanujan’s Class Invariant, Some Sectors of Particle Physics and Some Formulae Concerning the Supersymmetry

Authors: Michele Nardelli, Antonio Nardelli
Comments: 186 Pages.

In the present research thesis, we have obtained various and interesting mathematical connections with the Ramanujan’s numbers 1728, 1729, 728, 729 and some sectors of Particle Physics and Supersymmetry
Category: Mathematical Physics

[859] viXra:1905.0268 [pdf] submitted on 2019-05-17 17:43:20

Ecriture Détaillée Des Equations de la Relativité Générale :Cas D’Une Métrique Diagonale

Authors: Abdelmajid Ben Hadj Salem
Comments: 22 Pages. In French.

In this note, we study Einstein equations (EE) of general relativity considering a manifold M with a diagonal metric g_{ij}. We calculate the expression of the components of Ricci and Riemann tensors and the value of the scalar curvature R. Then we give the expression of the (EE) : -a- for the case where g_{ii}=g_i=g_i(x_i); -b- for the case where g_1=g_1(x_1=t) and g_i=g_i(t,x_i) for i=2,3,4$; -c- for the case (b) with x_4=z_0=constant.
Category: Mathematical Physics

[858] viXra:1905.0142 [pdf] submitted on 2019-05-09 19:53:08

(LFs and Gravity Working Paper Variant 1.0 7 Pages 13.04.2019) Life Forms, "Hybrid" Causality, Gravity and Hierarchical Parallel Universes

Authors: Andrei Lucian Dragoi
Comments: 7 Pages.

This paper proposes a new definition of life forms in relation to a new type of “hybrid” causality, gravity and the possible existence of hierarchical parallel universes. Keywords: life forms, gravity, hierarchical parallel universes;
Category: Mathematical Physics

[857] viXra:1905.0012 [pdf] submitted on 2019-05-01 14:07:09

A Mathematical Overview of Mass and Energy Conservation in Modern Physics

Authors: Dang Dang
Comments: 28 Pages.

The idea of energy, matter, and motion has perplexed many philosophers and physicists from antiquity to modern physics, from Plato to Einstein. New and developing physical theories raise different interpretations of energy and matter but no complete theory of everything exists at present. However, there is a law we can almost take for granted: the law of conservation of energy, which states that energy cannot be created nor destroyed although it can be transformed from one form to another. After establishing the foundational theory and history of conservation of energy, this literature review aims to provide an overview of the concept of mass and energy conservation in two of the most fundamental physical theories - quantum mechanics and general relativity. Consequences and challenges of mass-energy conservation and equivalence - dark energy - is studied in an introductory manner
Category: Mathematical Physics

[856] viXra:1904.0552 [pdf] submitted on 2019-04-28 12:51:07

Black Holes in a Rotating Hologram Universe.

Authors: Dan Visser
Comments: 7 Pages.

Black holes are not what it looks like due to postmodern Big Bang interpretations. In my new cosmology black holes are part of a rotating hologram-universe. The black hole mass-density thereto is replaced by my new parameter Tdan, which makes mass-density of a black hole independent of the light speed in vacuum according to general relativity. General relativity has to be extended by refining the Planck-units in a domain below the Planck-boundary. Tdan is that refining-mechanism.
Category: Mathematical Physics

[855] viXra:1904.0533 [pdf] submitted on 2019-04-27 12:56:38

On the Mathematical Formulation of 4D Fock Space

Authors: Paul Werbos
Comments: 6 Pages.

Ordinary Fock space, defined as concatenated combination of three-dimensional spaces is the main workhorse of the canonical version of quantum field theory. It is also fundamental to the modern version of quantum field theory without observers, as in the theory of Everett, Wheeler and Deutsch, which led to the theory of the universal quantum computer. It also has many practical uses, from quantum optics to the closure of turbulence and the derivation of the emergent behavior of space-time dynamical systems. But many of us believe that time and space are interchangeable to some degree, and that methods based on 4D Fock space are needed. This letter describes two simple mathematical tools to help make that possible. It discusses how computing the emergent statistics of such systems is a proper generalization of value function estimation in machine learning, which may therefore carry the same complexities with it.
Category: Mathematical Physics

[854] viXra:1904.0505 [pdf] submitted on 2019-04-25 07:57:08

Riemann's Definition for the Integrals in Mathematical Physics

Authors: Louiz Akram
Comments: 3 Pages.

This is my other work about the riemann Sum as a définition to the integral and the result is really important for many fields.
Category: Mathematical Physics

[853] viXra:1904.0503 [pdf] submitted on 2019-04-25 08:26:20

An Annex and Application for :Mémoire en Physiques.

Authors: Louiz Akram
Comments: 2 Pages.

Mémoire en physiques is a work made since January 2016 by Louiz Akram (an independant researcher).
Category: Mathematical Physics

[852] viXra:1904.0477 [pdf] submitted on 2019-04-24 08:37:09

Mémoire en Physiques

Authors: Louiz Akram
Comments: 30 Pages.

The derivation in the galilean was made in my work differently than the famous steps when dealing with relative rotations. My work gives the results with an accurate uncertainty and it is the only correct derivation for physics' use, hence, It is the solution to avoid the mistakes made when dealing with the Newtonian Mechanics and thus to avoid the relativity of Time.
Category: Mathematical Physics

[851] viXra:1904.0464 [pdf] submitted on 2019-04-24 15:42:36

A Disproof to the Time Dilation .

Authors: Louiz Akram
Comments: 2 Pages.

This a disproof to Einstein's special relativity and to Lorentz' Transformation .
Category: Mathematical Physics

[850] viXra:1904.0455 [pdf] submitted on 2019-04-23 08:24:27

From Maxwell’s Equations to the String Theory and Particle Physics: New Mathematical Connections with Some Sectors of Number Theory

Authors: Michele Nardelli, Antonio Nardelli
Comments: 179 Pages.

In this research thesis we have described some new mathematical connections between Maxwell’s Equations, some sectors of the String Theory and Particle Physics, and some sectors of Number Theory, precisely various Ramanujan’s expressions and equations.
Category: Mathematical Physics

[849] viXra:1904.0448 [pdf] submitted on 2019-04-23 13:43:14

On the Initial Chaos of the Universe: Using Null Deflection of Perturbation Element Over flat Geometry

Authors: Divyansh Mansukhani
Comments: 2 Pages.

While the flatness problem, Ω = 1, has been one weighty stand in the modern cosmology to showcase incompetency of BBT, the theory of inflation - first pioneered by Alan Guth, CTP, MIT (current) - serves to accommodate it in the observed universe. Here, (a) FP is used as a skeleton to attempt for an altogether novel approach involving rudimentary perturbation theory to define what one may call as ‘initial chaos’, and (b) the corresponding approach is postulated to be lightly rigorous than the other frameworks which propose in the same domain.
Category: Mathematical Physics

[848] viXra:1904.0340 [pdf] submitted on 2019-04-17 14:26:12

Completeness in Physics

Authors: Jeremy Dunning-Davies, Richard Lawrence Norman
Comments: 3 Pages.

Here it is intended to raise some questions surrounding the whole notion of completeness in physics. This does, of course, have bearing on issues raised by the well-known paper by Einstein, Podolsky and Rosen.
Category: Mathematical Physics

[847] viXra:1904.0268 [pdf] submitted on 2019-04-14 10:05:16

Spherical Harmonics and Crystals

Authors: Giuliano Bettini
Comments: 27 Pages. In Italian

The description of Point Groups is made in crystallography, among other, with "character tables". Following my classification work entitled "5 bit 32 crystal classes" and some other curious properties I've noticed, I wanted to try to find a representation with Spherical Harmonics namely: a set of 32 Spherical Harmonics each one representing a Point Group. So the purpose of this work, in a nutshell, is to combine each of the 32 crystal classes with the corresponding Spherical Harmonic that has the same symmetry properties, in a certain sense therefore a "group description". These are among all the Spherical Harmonics the only 32 with which it is possible to create periodic structures with no gaps nor overlapping. A sort of Spherical Harmonics Restriction Theorem. Other possibly interesting connections with the s p d f sub-shells, and with spin, are to be investigated.
Category: Mathematical Physics

[846] viXra:1904.0206 [pdf] submitted on 2019-04-10 06:49:14

The Origin of New Dark Energy.

Authors: Dan Visser
Comments: 13 Pages.

New dark energy is related to a new cosmological model (RTHU). This paper refers to the origin of this new dark energy. As a follow-up this paper considers why CERN (LHC), and other colliders, are relics of the past and why the RTHU-scanner will be the future. The RTHU stands for a rotating hologram universe. The details are anchored in my series of article hosted in the vixra-archive, category mathematical physics. Reach it on www.vixra.org/author/dan_visser. It represents my horizon, my art and my basic-science for the work-out of the new dark energy in the RTHU.
Category: Mathematical Physics

[845] viXra:1904.0183 [pdf] submitted on 2019-04-09 11:35:38

On the Integrability of Liénard Equations

Authors: Y.F. J. Kpomahou, M. D. Monsia
Comments: 4 pages

A simple condition for integrability of Liénard equations is established to compute their general solution explicitly or by quadrature via a nonlocal transformation.
Category: Mathematical Physics

[844] viXra:1904.0114 [pdf] submitted on 2019-04-05 09:50:38

Gravitational and Gravity Constans , and Their Physical Interpretation.

Authors: Markos Georgallides
Comments: 73 Pages.

In Mechanics Work = Energy = motion is [Force] x[Displacement] and is conserved . In order Motion is conserved as Displacement in all directions , then Displacement must be kept , Quantized , in a Finite Space differently is annihilated .The only possible motion in a Finite -Space is the Periodic-excitation [→ ←] and Revolving motion [(+)↻↺(-)] which is proved define the quality of Particles . Periodic excitation between Space (+) and Anti-Space (-) , may exist only as Collision of Opposite , and this because of the equal and opposite Point-charges that are infinitely close together which create Coulomb Electric dipole-moment in an Electric-field . Motion is captured in a [Box-P] called Stationary-Material-point containing these three elements [ (+) ,[↔], (-)] which are , Space , Energy , Anti-space . The Spin of this Dipole is Stationary and is proved to be the Gravity g . Revolving motion may exist between Space (+) and Anti-Space (-) so the Revolving of Two-Points A(+) and B(-) consist the Material-Point in Segment r = |AB| , and carries the Principal stress , σ , between , A , B , which stress σ as Centripetal acceleration is the Centripetal-force and the minimum Energy becoming from the in-storage [AB] acceleration and is proved to be equal to the Gravity-wave , g . The continually produced Work in this [Box-R] is stored in it as the Golden-ratio-frequency-motion , not eternally but Partially , and the rest superfluous motion is launched out the Box as an Propagating Electromagnetic-Wave , which Out-Wave carries the [Box–R] , and it is called the Photon . Local Spin of [Box-P] is oriented to that of [Box-R] , by a Local-uniform Pressure equal to , g * [Force/Area] = G , which is Newton-Universal-Gravitational-constant G force , such for Macrocosm as for Microcosm , and for both cases Obeying Newton`s Laws of motion . It was Proved that Force G is the Pressure on Gravity g , the First-kick-Start , to Enter Planck-cave and formulate in orbit of Planck`s cave , the lightest and the less-mass Particle of this universe which is the Hydrogen-cave . In the Undamped Planck`s – Conservative -System , Total-Energy of , -13,6 eV , of Hydrogen , corresponds to the Natural-frequency of the Primary-Particle with the less Negative-charge-frequency, and this is The Electron , e , which mass and frequency follows min.- g . In the Extreme -Three-Body-Problem case ,where any two massive bodies infinitely close together consist a Slit , The-Slit-Focus , is then created a New Structure for Atom as in article [77] which Properties and Configuration anomalies dependent on , e , p , n , numbers. Since Force G is a Uniform-Pointy–Force , therefore needs a Conductor , a Layer , a kind of mass , to be spread and act on it as Stress = Surface-force , which is the Layer or the Conductor of Spin S , or the Stress g , and this because of Stress-Layer, g , where all the Energy-Structures present mass . Gravity acceleration , g , produced from the in Material-points acceleration is equal to the pressure , σ , i.e. the Conductor to all Waves as , Force G - ON-Layer - A , [A = m x g] , = Gravity .
Category: Mathematical Physics

[843] viXra:1904.0073 [pdf] submitted on 2019-04-03 08:09:11

Non-commutativity: Unusual View

Authors: Valeriy V. Dvoeglazov
Comments: 4 Pages. Prog. Phys. 15 (2019) 48-51

Some ambiguities have recently been found in the definition of the partial derivative (in the case of presence of both explicit and implicit dependencies of the function subjected to differentiation). We investigate the possible influence of this subject on quantum mechanics and the classical/quantum field theory. Surprisingly, some commutators of operators of space-time 4-coordinates and those of 4-momenta are not equal to zero. We postulate the non-commutativity of 4-momenta and we derive mass splitting in the Dirac equation. Moreover, two iterated limits may not commute each other, in general. Thus, we present an example when the massless limit of the function of E, p, m does not exist in some calculations within quantum field theory
Category: Mathematical Physics

[842] viXra:1903.0429 [pdf] submitted on 2019-03-25 04:20:29

On the Wave Motion and Inertial Mass of Quantum Particles

Authors: Vu B Ho
Comments: 9 Pages.

In this work we will discuss the possibility that if a quantum particle possesses a fluid state, as shown in our work on the fluid state of Dirac quantum particles, then the motion of the physical particle in an ambient space may be directly related to its fluid state and therefore it can be explained in terms of the wave motion of physical objects that move in a substrate space with the mechanism similar to that of peristaltic locomotion. In particular, we will also discuss the possibility that the so-called inertial mass of a particle in classical physics may be identified as a form of gripping connection between the particle and the substrate, which is the ambient space itself, that is needed for a particle to move in space. This is similar to a tight grip that is needed for a physical object to move on a surface.
Category: Mathematical Physics

[841] viXra:1903.0419 [pdf] submitted on 2019-03-23 11:42:35

On the General Solution for the Quintic Duffing Oscillator Equation

Authors: J. Akande, D. K. K. Adjaï, Y. J. F. Kpomahou, M. D. Monsia
Comments: 4 pages

This paper shows for the first time that exact and general solution for the quintic Duffing oscillator equation may be computed in a straightforward manner within the framework of the generalized Sundman transformation theory introduced recently by authors of this work. A major advantage of the applied method is that it intimately relates such an oscillator equation to the quadratic anharmonic oscillator equation with well-known exact solutions.
Category: Mathematical Physics

[840] viXra:1903.0385 [pdf] submitted on 2019-03-22 05:56:29

The Mathematical Universe

Authors: Manjunath.R
Comments: 462 Pages.

We Humans, a curious beings developed from the Darwin’s principle of natural selection, are accustomed into an inquisition. The question is not ‘do we know everything from the triumph of the Higgs boson to the underlying discomfort of ultimate question of life, the universe, and everything?’ or it is ‘do we know enough?’ But how the creative principle resides in mathematics? There’s something very mathematical about our gigantic Cosmos, and that the more carefully we look, the more equations are built into nature: our universe isn’t just described by math, but that universe is a “grand book” written in the language of mathematics. We find it very appropriate that mathematics has played a striking role in our growing understanding of the events around us, and of our own existence.
Category: Mathematical Physics

[839] viXra:1903.0255 [pdf] submitted on 2019-03-13 16:31:06

Resurrection of the Dead and the Organization of the Society of Electronic e-Beings.

Authors: Olga Lyubavina, Alexander Bolonkin
Comments: 9 Pages.

Alexander Bolonkin in his works [1-7] proposed methods of electronic immortality of modern people. He predicted the gradual replacement of biological humanity E-beings, considered their advantages and disadvantages (see List of references in given articles). The author considers methods and modern possibilities of resurrection of long-dead outstanding personalities. It also considers the principles and organization of the new E-society, its goals and conditions of existence.
Category: Mathematical Physics

Replacements of recent Submissions

[686] viXra:1908.0286 [pdf] replaced on 2019-08-15 17:26:00

A New Appraoch to Proof the Riemann Hypothesis Using New Operator

Authors: Rafik Zeraoulia
Comments: 09 Pages. no comment

In this note we present a new approach to proof the Riemann hypothesis one of the most important open problem in pure mathematics using a new operator derived from unitary operator groups acts on Riemann-Siegal function and it uses partition function for Hamiltonian operator , The interest idea is to compute the compositional inverse of Riemann zeta function at $s=-\frac12$ such as we show that:$\zeta^{-1}(-\frac12) =\zeta(\frac12+i \beta)=0$ for some $\beta >0 $
Category: Mathematical Physics

[685] viXra:1907.0398 [pdf] replaced on 2019-08-09 12:34:51

Energy-Momentum is not Defined Globally, But Locally

Authors: Dmitri Martila
Comments: 12 Pages.

Slow precession of the Earth rotation axis, and the Moon-Earth orbital resonance were accompanied during centuries by Newton's and Laplace's explanations. However, in the present paper, the author considers the possibility of additional factor: the small violation of the global energy-momentum conservation. Thus, the energy-momentum concept being not conserved, cannot be regarded as total (global) energy-momentum of system. The recently experimentally verified Lense-Thirring Effect and the Mercury's perihelion anomalous shift cannot be found in Newton Physics, and the latter demands the global energy-momentum conservation. Thus, the shift violates global energy-momentum conservation. Why? Because the energy-momentum is defined locally, not globally.
Category: Mathematical Physics

[684] viXra:1906.0512 [pdf] replaced on 2019-07-22 14:14:40

An Axiomatic Model of Science

Authors: Alexandre Harvey-Tremblay
Comments: 42 Pages.

Here we present a mathematical model formalizing the practice of science in nature. Under the premise that science is the best methodology to understand the World, then presumably a formalization of such is its best mathematical framework. Axiomatic science is a significant improvement over the informal practice of science and it has numerous desirable properties. Axiomatic science is a model of science and of physics, and as such, it contains a 'science' part and a 'physics' part. Axiomatic science is able to derive the 'physics' part, including the laws of physics, using the 'science' part as the starting point. Axiomatic science thus explains the origins of the laws of physics as a theorem of the formal practice of science. Finally, axiomatic science is 'clarification tool par excellence' for the foundation of physics.
Category: Mathematical Physics

[683] viXra:1906.0239 [pdf] replaced on 2019-06-16 10:24:38

A Mathematical Expression for Inverse Fine-Structure Constant

Authors: Alan Michael Gómez Calderón
Comments: 2 Pages.

From the golden angle and the Pell constant, a simple, elegant and concise mathematical expression of the inverse fine-structure constant is given.
Category: Mathematical Physics

[682] viXra:1906.0214 [pdf] replaced on 2019-07-08 10:14:43

Exact Periodic Solutions of Truly Nonlinear Oscillator Equations and Quadratic Liénard-Type Equations

Authors: Y. J. F. Kpomahou, L. H. Koudahoun, K. K. D. Adjaï, J. Akande, M. D. Monsia
Comments: 15 pages

The present research contribution is devoted to solving the integrability problem of Liénard type differential equations. It is shown that such a problem may be solved by nonlocal transformation for some classes of equations. By doing so, it is observed that the integrability of a class of restricted Duffing type equations with integral power or fractional power nonlinearity may be secured by that of a general class of quadratic Liénard type differential equation, and vice versa. Such a restricted Duffing type equation is also shown to be closely related to a quadratic Li´enard type equation for which exact and explicit general solution may be computed. In this context it has been shown that exact and general periodic solutions may be computed for these two classes of restricted Duffing equations and quadratic Liénard type equations. The comparison of obtained solutions with some well-known results is carried out in some cases.
Category: Mathematical Physics

[681] viXra:1906.0212 [pdf] replaced on 2019-07-08 10:22:02

Integrability Analysis of a Generalized Truly Nonlinear Oscillator Equation

Authors: L. H. Koudahoun, Y. J. F. Kpomahou, J. Akande, K. K. D. Adjaï, M. D. Monsia
Comments: 5 pages

The integrability of a general class of Liénard type equations is investigated through equation transformation theory. In this way it is shown that such a class of Liénard equations can generate a generalization of some interesting truly nonlinear oscillator equations like the cube and fifth root differential equations. It has then become possible to compute the exact and general solution to the generalized truly nonlinear oscillator equation. Under an appropriate choice of initial conditions, exact and explicit solution has been obtained in terms of Jacobi elliptic functions.
Category: Mathematical Physics

[680] viXra:1904.0533 [pdf] replaced on 2019-04-28 11:29:31

On the Mathematical Formulation of 4D Fock Space

Authors: Paul Werbos
Comments: 6 Pages. word screwed up eq 2 in v1. Replaced word equation with image object.

Ordinary Fock space, defined as concatenated combination of three-dimensional spaces is the main workhorse of the canonical version of quantum field theory. It is also fundamental to the modern version of quantum field theory without observers, as in the theory of Everett, Wheeler and Deutsch, which led to the theory of the universal quantum computer. It also has many practical uses, from quantum optics to the closure of turbulence and the derivation of the emergent behavior of space-time dynamical systems. But many of us believe that time and space are interchangeable to some degree, and that methods based on 4D Fock space are needed. This letter describes two simple mathematical tools to help make that possible. It discusses how computing the emergent statistics of such systems is a proper generalization of value function estimation in machine learning, which may therefore carry the same complexities with it.
Category: Mathematical Physics

[679] viXra:1904.0315 [pdf] replaced on 2019-08-13 11:09:47

Time and Continuum: Zenon Manifold

Authors: D. Chakalov
Comments: 31 Pages. Comments welcome.

Ensuing from first principles, I suggest pre-geometric theory of spacetime, in which the apex of light cone ‘here and now’ is not modeled with dimensionless point, but with non-trivial mathematical object along null intervals, endowed with brand new structure, topology and dynamics, and defined on so-called Zenon manifold. To that end, I offer proposals relevant to Mathematics and mathematical physics, a new model of spacetime (pp. 10-12), my opinion of gravitational radiation (pp. 13-15), and speculations about spacetime engineering (pp. 16-31).
Category: Mathematical Physics

[678] viXra:1904.0315 [pdf] replaced on 2019-06-22 06:38:03

Time and Continuum: Zenon Manifold

Authors: D. Chakalov
Comments: 18 Pages. Comments welcome.

Ensuing from first principles, I suggest pre-geometric theory of spacetime, in which the apex of light cone ‘here and now’ is not modeled with dimensionless point, but with non-trivial mathematical object along null intervals, endowed with brand new structure, topology and dynamics, and defined on so-called Zenon manifold. To that end, I offer three proposals relevant to Mathematics and mathematical physics, a new model of spacetime (pp. 10-12), and my opinion of gravitational radiation (pp. 13-15).
Category: Mathematical Physics

[677] viXra:1904.0315 [pdf] replaced on 2019-06-14 06:09:58

Time and Continuum: Zenon Manifold

Authors: D. Chakalov
Comments: 16 Pages. Comments welcome.

Ensuing from first principles, I suggest pre-geometric theory of spacetime, in which the apex of light cone ‘here and now’ is not modeled with dimensionless point, but with non-trivial mathematical object along null intervals, endowed with brand new structure, topology and dynamics, and defined on so-called Zenon manifold. To that end, I offer three proposals relevant to Mathematics and mathematical physics, a new model of spacetime (pp. 10-12), and my opinion of gravitational radiation (pp. 13-15).
Category: Mathematical Physics

[676] viXra:1904.0315 [pdf] replaced on 2019-06-07 11:07:21

Time and Continuum: Zenon Manifold

Authors: D. Chakalov
Comments: 14 Pages. Comments welcome.

Ensuing from first principles, I suggest pre-geometric theory of spacetime, in which the apex of light cone ‘here and now’ is not modeled with dimensionless point, but with non-trivial mathematical object along null intervals, endowed with brand new structure, topology and dynamics, and defined on so-called Zenon manifold. To that end, I offer three proposals relevant to Mathematics and mathematical physics, a new model of spacetime (pp. 10-12), and my personal opinion on gravitational radiation (pp. 13-14).
Category: Mathematical Physics

[675] viXra:1904.0315 [pdf] replaced on 2019-06-01 22:25:30

Time and Continuum: Zenon Manifold

Authors: D. Chakalov
Comments: 12 Pages. Final version.

Ensuing from first principles, I suggest pre-geometric theory of spacetime, in which the apex of light cone ‘here and now’ is not modeled with dimensionless point, but with non-trivial mathematical object along null intervals, endowed with brand new structure, topology and dynamics, and defined on so-called Zenon manifold. To that end, I offer three proposals relevant to Mathematics and mathematical physics, and a new model of spacetime (pp. 10-12).
Category: Mathematical Physics

[674] viXra:1904.0315 [pdf] replaced on 2019-05-30 07:35:34

Time and Continuum: Zenon Manifold

Authors: D. Chakalov
Comments: 11 Pages. Comments welcome.

Ensuing from first principles, I suggest pre-geometric theory of spacetime, in which the apex of light cone ‘here and now’ is not modeled with dimensionless point, but with non-trivial mathematical object along null intervals, endowed with brand new structure, topology and dynamics, and defined on so-called Zenon manifold. To that end, I offer three proposals relevant to Mathematics and mathematical physics, and a new model of spacetime (pp. 10-11).
Category: Mathematical Physics

[673] viXra:1904.0315 [pdf] replaced on 2019-05-27 09:26:06

Time and Continuum: Zenon Manifold

Authors: D. Chakalov
Comments: 9 Pages. Text expanded and typos corrected.

Ensuing from first principles, I suggest pre-geometric theory of spacetime, in which the apex of light cone ‘here and now’ is not modeled with dimensionless point, but with non-trivial mathematical object along null intervals, endowed with brand new structure, topology and dynamics, and defined on so-called Zenon manifold. To that end, I suggest three proposals relevant to Mathematics and mathematical physics.
Category: Mathematical Physics

[672] viXra:1904.0315 [pdf] replaced on 2019-05-23 07:38:21

Time and Continuum: Zenon Manifold

Authors: D. Chakalov
Comments: 9 Pages. Comments welcome.

Ensuing from first principles, I suggest pre-geometric theory of spacetime, in which the apex of light cone ‘here and now’ is not modeled with dimensionless point, but with non-trivial mathematical object along null intervals, endowed with brand new structure, topology and dynamics, and defined on so-called Zenon manifold. To that end, I suggest three proposals relevant to Mathematics and mathematical physics.
Category: Mathematical Physics

[671] viXra:1904.0315 [pdf] replaced on 2019-05-19 17:38:04

Time and Continuum: Zenon Manifold

Authors: D. Chakalov
Comments: 8 Pages. Comments welcome.

Ensuing from first principles, I suggest pre-geometric theory of spacetime, in which the apex of light cone ‘here and now’ is not modeled with dimensionless point, but with non-trivial mathematical object along null intervals, endowed with brand new structure, topology and dynamics, and defined on so-called Zenon manifold.
Category: Mathematical Physics

[670] viXra:1904.0268 [pdf] replaced on 2019-04-21 10:22:35

Spherical Harmonics and Crystals

Authors: Giuliano Bettini
Comments: 27 Pages. In English. Updated.

The description of Point Groups is made in crystallography, among other, with "character tables". Following my classification work entitled "5 bit 32 crystal classes" and some other curious properties I've noticed, I wanted to try to find a representation with Spherical Harmonics namely: a set of 32 Spherical Harmonics each one representing a Point Group. So the purpose of this work, in a nutshell, is to combine each of the 32 crystal classes with the corresponding Spherical Harmonic that has the same symmetry properties, in a certain sense therefore a "group description". These are among all the Spherical Harmonics the only 32 with which it is possible to create periodic structures with no gaps nor overlapping. A sort of Spherical Harmonics Restriction Theorem. Other possibly interesting connections with the s p d f sub-shells, and with spin, are to be investigated.
Category: Mathematical Physics

[669] viXra:1904.0268 [pdf] replaced on 2019-04-20 01:43:00

Spherical Harmonics and Crystals

Authors: Giuliano Bettini
Comments: 27 Pages. In Italian. This is the update to the Italian version v1.

The description of Point Groups is made in crystallography, among other, with "character tables". Following my classification work entitled "5 bit 32 crystal classes" and some other curious properties I've noticed, I wanted to try to find a representation with Spherical Harmonics namely: a set of 32 Spherical Harmonics each one representing a Point Group. So the purpose of this work, in a nutshell, is to combine each of the 32 crystal classes with the corresponding Spherical Harmonic that has the same symmetry properties, in a certain sense therefore a "group description". These are among all the Spherical Harmonics the only 32 with which it is possible to create periodic structures with no gaps nor overlapping. A sort of Spherical Harmonics Restriction Theorem. Other possibly interesting connections with the s p d f sub-shells, and with spin, are to be investigated.
Category: Mathematical Physics

[668] viXra:1904.0218 [pdf] replaced on 2019-04-19 07:37:16

Back to Cosmos

Authors: F.M. Sanchez, V. Kotov, M. Grosmann, D. Weigel, R. Veysseyre, C. Bizouard, N. Flawisky, D. Gayral, L. Gueroult
Comments: 27 Pages. To be published in Progress in Physics

To the memory of Sir Michael Atiyah Abstract. The ancestral concept of Cosmos is rediscovered through the idea of a Tachyonic Grandcosmos Multibasis Computer, inversing the Anthropic Principle and reestablishing the Laplace Determinism. The observed fine tuning between physical dimensionless parameters is interpreted as relations between optimal calculation basis, announcing a dramatic progress in computer software. Three type of mathematical constants are considered: Large, Intermediate and close to unity. The famous Large Number problem is resolved by Eddington's statistical theory and the gravitational Hydrogen Molecule model, leading to the visible Universe horizon radius R ≈ 13.812 Giga ligth-years. The extension of the double cosmic correlation defines a Topological Axis using Euler-Napier constant e as primary basis, confirming String Theory, Cartan-Bott periodicity and the 30 holic dimensions corresponding to the simplest space-time-matter diophantine equation T^2 = L^3 = M^5 = N^30. This dimension n = 30 corresponds to the common time, about 10^58 s, given by two mandatory dimensional analysis, interpreted as the Supercycle period. The visible Universe wavelength 'Topon' 2Għ/Rc3 ≈ 4 × 10^-96 m corresponds to n ≈ 2ee and enters the 1D mono-radial holographic extension of the Bekenstein-Hawking Universe entropy, implying the critical condition, and breaking the Planck wall by a factor 1061, justifying the Hawking trans-planckian frequencies. The monochrome holographic extension leads to a Grandcosmos, larger than the visible Universe by the same factor 10^61. A toponic quantization justifies the Cosmos vastness in a scanned Universe, justifying the entropy factor 1/4. This implies a tachyonic speed in the same ratio by respect to c, justifying the Planck re-normalisation of the vacuum energy, independently checked by the Casimir effect. The couple Universe-Grandcosmos is confirmed by a dramatic geo-dimensional analysis, where Length, Time and Mass ratios are considered as unit vectors in a 3D Super-space. A matter-antimatter 10^104 Hz Oscillatory Bounce unifies standard Single Bang with steady-state cosmology, but suppress Relativity in cosmology at large, reestablishing the Newton Absolute Space realized by the Microwave Cosmic Radiation, while Kotov cycle defines a quasi-absolute clock. This new scanning space-time structure is confirmed by single-electron cosmology, connected with Kotov period, and relying Sternheimer Biological scale factor and Atiyah constant, which appear as privileged computation basis, as well as e, p and a ≈ 137.036, in liaison with the sporadic groups. The Atiyah constant enters dramatic ppb precision relations with particle data. This unifies mathematics, physics, chemistry, biology and philosophy. It is predicted that the future telescopes will find mature galaxies in the very far range, instead of a Dark Space, ruining the standard evolutionary cosmology, ill-founded on an imperfect Cosmological Principle.
Category: Mathematical Physics

[667] viXra:1904.0218 [pdf] replaced on 2019-04-17 12:18:01

Back to Cosmos

Authors: F.M. Sanchez, V. Kotov, M. Grosmann, D. Weigel, R. Veysseyre, C. Bizouard, N. Flawisky, D. Gayral, L. Gueroult
Comments: 26 Pages. Accepted by Progress in Ohysics, Avril 2019

To the memory of Sir Michael Atiyah Abstract. The ancestral concept of Cosmos is rediscovered through the idea of a Tachyonic Grandcosmos Multibasis Computer, inversing the Anthropic Principle and reestablishing the Laplace Determinism. The observed fine tuning between physical dimensionless parameters is interpreted as relations between optimal calculation basis, announcing a dramatic progress in computer software. Three type of mathematical constants are considered: Large, Intermediate and close to unity. The famous Large Number problem is resolved by Eddington's statistical theory and the gravitational Hydrogen Molecule model, leading to the visible Universe horizon radius R ≈ 13.812 Giga ligth-years. The extension of the double cosmic correlation defines a Topological Axis using Euler-Napier constant e as primary basis, confirming String Theory, Cartan-Bott periodicity and the 30 holic dimensions corresponding to the simplest space-time-matter diophantine equation T2 = L3 = M5 = N30. This dimension n = 30 corresponds to the common time, about 10^58 s, given by two mandatory dimensional analysis, interpreted as the Supercycle period. The visible Universe wavelength 'Topon' 2Għ/Rc3 ≈ 4 × 10^-96 m corresponds to n ≈ 2ee and enters the 1D mono-radial holographic extension of the Bekenstein-Hawking Universe entropy, implying the critical condition, and breaking the Planck wall by a factor 10^61, justifying the Hawking trans-planckian frequencies. The monochrome holographic extension leads to a Grandcosmos, larger than the visible Universe by the same factor 10^61. A toponic quantization justifies the Cosmos vastness in a scanned Universe, justifying the entropy factor 1/4. This implies a tachyonic speed in the same ratio by respect to c, justifying the Planck re-normalisation of the vacuum energy, independently checked by the Casimir effect. The couple Universe-Grandcosmos is confirmed by a dramatic geo-dimensional analysis, where Length, Time and Mass ratios are considered as unit vectors in a 3D Super-space. A matter-antimatter 10^104 Hz Oscillatory Bounce unifies standard Single Bang with steady-state cosmology, but suppress Relativity in cosmology at large, reestablishing the Newton Absolute Space realized by the Microwave Cosmic Radiation, while Kotov cycle defines a quasi-absolute clock. This new scanning space-time structure is confirmed by single-electron cosmology, connected with Kotov period, and relying Sternheimer Biological scale factor and Atiyah constant, which appear as privileged computation basis, as well as e, p and a ≈ 137.036, in liaison with the sporadic groups. The Atiyah constant enters dramatic ppb precision relations with particle data. This predicts unification of mathematics, informatics, physics, chemistry, biology and philosophy. The future telescopes will find mature galaxies in the very far range, instead of a Dark Space, ruining the standard evolutionary cosmology, ill-founded on an imperfect Cosmological Principle.
Category: Mathematical Physics