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[7] viXra:2510.0144 [pdf] replaced on 2025-11-02 14:27:21
Authors: Ervin Goldfain
Comments: 40 Pages.
Complex Ginzburg-Landau equation (CGLE) is a universal amplitude equation governing the dynamics of phenomena unfolding in far-from-equilibrium conditions. It was recently argued that CGLE emerges from primordial dimensional fluctuations acting in the far ultraviolet sector of field theory and primordial cosmology. Here we show that classical Maxwell, Dirac and non-Abelian field theories can be derived directly from a generalized version of CGLE without invoking a Lagrangian or variational principle. Demanding that CGLE preserves local coherence under continuous internal transformations, we introduce a natural covariant derivative whose connection acts as a gauge field. The commutator of these covariant derivatives defines a curvature tensor that reproduces the familiar structure of Maxwell and Yang—Mills field strengths, while a first-order, spinor generalization of CGLE yields Dirac-type dynamics. In a nutshell, classical field theories naturally emerge from demanding local coherence invariance of the generalized CGLE.
Category: Mathematical Physics
[6] viXra:2510.0105 [pdf] submitted on 2025-10-21 20:46:23
Authors: Ulrich Schreier
Comments: 12 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This paper introduces Anton Bopp's (1900--1971) comprehensive vibratory-hydro-dynamic model to the international scientific community. Bopp's unpublished manuscripts present a unified theory spanning cosmic to atomic and subatomic scales, using the hydrogen atom as a universal archetype. The model demonstrates a remarkable capacity to derive fundamental physical constants through mathematical relationships involving the foundational set ${pi, e, 1, 2, 3}$. While Bopp's primary focus was operational---developing practical tools for physical applications---his work reveals, as a natural byproduct, deep connections between mathematical principles and physical reality. This paper highlights selected findings of particular significance, situating Bopp's contributions within the historical continuum from Pythagorean harmony to Wigner's "unreasonable effectiveness of mathematics," suggesting that physical laws emerge from mathematical substrates rather than merely being described by them.
Category: Mathematical Physics
[5] viXra:2510.0087 [pdf] submitted on 2025-10-16 05:45:49
Authors: Taiwei Song
Comments: 8 Pages.
Based on the Geometry of Space-Time Structures founded by the author himself, this paper uses an accurate mathematical model to explain the space warp problem of the giant world, deduces the curvature formula of the optical path curve of the natural space-time space, and explains its physical significance; demonstrates the space-time transformation relationship between the geometric scene of natural space-time space and the visual image of the observer, and gives the space-time transformation equation; discusses the natural properties of the cosmic redshift, derives the redshift differential formula; proposes the experimental methods to verify the new space-time relationships of photons, etc.
Category: Mathematical Physics
[4] viXra:2510.0080 [pdf] replaced on 2025-11-12 23:21:50
Authors: James Johan Sebastian Allen
Comments: 66 pages. English. Updated operator formulation and equilibrium proof. Includes revised references and appendices.
This paper presents a functional proof strategy for the Riemann Hypothesis within the Pattern Field Theory framework, using the Allen Orbital Lattice (AOL) as the geometric and arithmetic substrate. The approach establishes an equivalence between two independently constructed systems: the continuous Equilibrion Hamiltonian, which describes recursive curvature balance along the critical line, and the discrete AOL operator, whose prime-anchored spectrum exhibits Gaussian Unitary Ensemble statistics after unfolding.The analysis shows that both systems produce self-adjoint spectra aligned to Re(s)=1/2, with nontrivial zeros interpreted as equilibrium nodes of the prime field. The operator includes prime-weighted potentials and duplex curvature phases, producing spectral behavior consistent with Riemann-class dynamics. Numerical diagnostics across 30—50 lattice shells confirm Wigner—Dyson spacing, with Kolmogorov—Smirnov and Cramér—von Mises distances stable under randomized phase ensembles. Control experiments removing the prime anchors fail to reproduce this universality, isolating prime weighting as a necessary structural condition.The paper incorporates the updated operator formulation, extended curvature analysis, and cross-references to related Pattern Field Theory results, including the conduction constant tau = 71.2 ± 3.9 ms measured during Pattern Alignment Lock formation. These results support the claim that the prime-indexed curvature harmonics on the AOL constitute a physical equilibrium field and that the Riemann Hypothesis corresponds to its stationary manifold.The work integrates mathematical, geometric, and empirical components into a unified framework and provides a stable model linking prime recursion to field equilibrium. This version includes updated references, consistency corrections, and the completed analytic—geometric correspondence across the continuous and discrete representations.
Category: Mathematical Physics
[3] viXra:2510.0067 [pdf] submitted on 2025-10-13 00:56:21
Authors: Udo E. Steinemann
Comments: 16 Pages.
Movement-patterns of geodesics are compared who firstly are conceived for masses floating mentally through space-time inside earth and secondly can be observed for spice-grains in kneaded dough.
Category: Mathematical Physics
[2] viXra:2510.0031 [pdf] submitted on 2025-10-06 14:42:59
Authors: Julio Jaramillo
Comments: 13 Pages.
This work introduces a unified operator framework for quantum field theory through the emph{generalized relativistic wave differential operator} $D^{mnlambda}_{alphabeta}$. By appropriate parameter choices, this operator encompasses the Klein-Gordon, Dirac, and non-monogenic operators, revealing their fundamental connections. We propose a emph{quantum field tensor} $Psi_{sigmahotau}$ with binary activation indices for scalar, spinor, and gauge fields, generating all possible interactions while preserving Lorentz covariance. The framework incorporates gauge invariance through minimal coupling and yields both Proca and Maxwell equations as special cases. This approach provides a powerful operator-based unification of quantum field theory with applications to higher-spin theories.
Category: Mathematical Physics
[1] viXra:2510.0013 [pdf] submitted on 2025-10-04 12:39:32
Authors: Thierry L. A. Periat
Comments: 62 Pages. In French: Les matrices périennes ordinaires - lien avec le problème des trois générations de particules
The belief that one may unify physics, especially the theories concerning electromagnetism and gravitation, motivated my first intuitive ideas in 2003. I reanalyse the way of thinking which has been introduced in the initial document because it is in fact at the origin of the so-called (E) question. The search for answers to this question has allowed the development of diverse methods explaining how to divide (decompose) deformed cross products. It turns out that the kerns of the main parts of the decompositions have remarkable properties, useful in particle physics. This is what this document demonstrates since it succeeds in proving a link between a set of ordinary perian matrices and the mass-matrices proposed twenty-five years ago by theoreticians. The approach I have developed over the past quarter century therefore provides an algebraic and geometric explanation for the matrices which had been proposed by the physicists with the inner logic of particle physics. It helps to give particles a concrete face.FR version - Ma croyance en la possibilité d'unifier les théories de l'électromagnétisme et de la gravitation m'avait motivé à présenter quelques idées en 2003. Je reviens ici sur le raisonnement sous-jacent au document initial parce que c'est lui qui a justifié la naissance de la question dite (E). La recherche de réponse à cette question a permis le développement de méthodes mathématiques qui toutes avaient l'espoir de généraliser la formule initiale. L'étude répétée et approfondie des réponses apportées montre que les noyaux des parties principales des décompositions des produits vectoriels déformés ont des propriétés mathématiques remarquables et utilisables en physique. C'est bien ce que ce document finit par démontrer puisqu'il établit enfin un lien clair entre un ensemble particulier de matrices périennes ordinaires et les matrices des masses proposées il y a maintenant plus de vingt-cinq ans par théoriciens de la physique. L'approche que j'ai développé au cours du quart de siècle passé fournit donc une explication algébrique et géométrique à des matrices qui résultaient jusque-là de la logique interne du modèle standard des particules. Elle contribue ainsi à leur donner un visage plus concret.
Category: Mathematical Physics
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