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| viXra.org > Mathematical Physics > 2602 |
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[7] viXra:2602.0115 [pdf] submitted on 2026-02-21 03:12:43
Authors: Jaykov Foukzon
Comments: 271 Pages.
Functional analysis works with TVS (Topological Vector Spaces), classically over archimedean fields like ℝ and ℂ.Canonical non-Archimedeanfunctional analysis, where alternative but equally valid number systems such as p-adic numbers ℚ_{p} etc. are fundamental, is a fast-growing discipline.This paper deals with TVS over non-classical non-Archimedean fields ^{∗}ℝ_{c}^{} ,^{∗}ℝ_{c}^{} and^{∗}ℂ_{c}^{}, ^{∗}ℂ_{c}^{}. Definitions and theorems related to non-Archimedean functional analysis onnon-Archemedean field ┊^{∗}ℝ_{c}^{}┊ and on complex field ┊^{∗}ℂ_{c}^{}┊=┊^{∗}ℝ_{c}^{}┊+i┊^{∗}ℝ_{c}^{}┊are considered. Applications to constructive quantum field theory also are considered
Category: Mathematical Physics
[6] viXra:2602.0114 [pdf] replaced on 2026-02-27 15:40:49
Authors: Ervin Goldfain
Comments: 34 Pages.
We show that dimensional regularization of a generic self-interacting field theory inducesan infrared mass scale, when the running spacetime dimension approaches the criticalvalue �� = 4. The mechanism is universal and does not rely on spontaneous symmetrybreaking alone. Instead, it arises from logarithmic corrections generated byrenormalization group (RG) flow near the bifurcation point at �� ≡ 4 − �� → 0. Weexplicitly indicate how dimensional transmutation converts marginal couplings intodynamically generated mass scales. This framework unifies the origin of the Higgsvacuum expectation value and electroweak boson masses with the Yang—Mills mass gapand the QCD scale ΛQCD. Step-by-step derivations are provided, without appealing tononperturbative assumptions beyond RG consistency. The paper focuses on the regimebordering relativistic quantum field theory and complex dynamics.
Category: Mathematical Physics
[5] viXra:2602.0112 [pdf] submitted on 2026-02-21 19:49:34
Authors: Jinyong Liu
Comments: 13 Pages. (Note by viXra Admin: For the last time, please cite and list scientific references!)
This paper addresses a classic core challenge in celestial mechanics—the three-body problem. Based on the fundamental axioms of Newtonian mechanics, we rigorously derive and prove a universal "Gravitational Superposition Theorem." This theorem states that the total gravitational field produced at any point in the external space by a finite set of point masses is completely equivalent to the gravitational field produced by a single point mass located at the system's center of mass, with a mass equal to the sum of the individual masses. Using this theorem as a cornerstone, the classical three-body problem can be precisely reduced to three strictly analytically solvable two-body relative motion problems.This research not only provides a theoretically self-consistent and mathematically complete framework for the long-standing three-body problem but also fundamentally reconstructs the theoretical paradigm and logical starting point for modeling multi-body gravitational systems.
Category: Mathematical Physics
[4] viXra:2602.0066 [pdf] submitted on 2026-02-09 21:36:20
Authors: Viktor Strohm
Comments: 4 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
The law of force governing the motion of a material point along an elliptical orbit is derived using a purely kinematic approach. Starting from the differential equations of motion in a Cartesian coordinate system, an angular equation of motion is obtained that directly leads to Kepler’s second law. It is shown that the acceleration is directed toward the focus of the ellipse and is inversely proportional to the square of the distance. The derived expressions are applied to the Earth—Moon system. Forces calculated using Newton’s second law are compared with those given by Newton’s law of universal gravitation. The relative discrepancy does not exceed 1.1%, confirming their equivalence.
Category: Mathematical Physics
[3] viXra:2602.0056 [pdf] submitted on 2026-02-08 17:19:27
Authors: Diego Cordoba Gazolaz, Luis Martinez Zoroa, Abdelmajid Ben Hadj Salem
Comments: 19 Pages. In French, the article was translated from spanish.
The Euler and Navier-Stokes equations describe the motion of fluids, but it is still unknown whether their smooth solutions (with $C^{infty}$ regularity) can develop singularities in finite time.This enigma, one of the «Millennium Prize Problems», poses fundamental mathematical and physical challenges. In this article, we review what singularities are, the main mechanisms proposed for their formation (selfsimilar solutions and vorticity cascades) as well as recent advances that shed new light on this problem in three dimensions.
Category: Mathematical Physics
[2] viXra:2602.0051 [pdf] submitted on 2026-02-07 23:55:14
Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 30 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org!)
The classical three—body problem is traditionally formulated as the predictionof complete spatial trajectories of three interacting masses under gravitation, a taskknown to be generally non—integrable and chaotic. In this work, we adopt a complementary perspective focused on the Sun—Earth—Moon system, where the most stable and observable features arise not from translational motion but from rotational recurrence and angular phase closure. We introduce an angular—toroidal phaseformalism in which the three bodies are represented by periodic phase variablesassociated with Earth rotation, Earth orbital motion, and lunar orbital motion. These phases naturally define a three—torus T3, within which the system evolves as a helical flow. Observable cycles such as the solar day, the synodic month, and the year emerge as alignment events corresponding to phase closure conditions. An alignment operator is proposed to characterize the temporal coherence of these events. The approach does not aim to recover full three—body trajectories, but in stead provides an analytic and geometrically transparent description of recurrence and temporal structure in the restricted three—body problem.
Category: Mathematical Physics
[1] viXra:2602.0017 [pdf] submitted on 2026-02-03 18:14:55
Authors: Goutham Netha Anagandula
Comments: 2 Pages. Pedagogical derivation connecting the Gambler's Fallacy to Gauge Invariance
The "Gambler’s Fallacy" is often treated as a cognitive bias, but it can be rigorously understood as a violation of translational invariance in probability space. In this paper, we define a "Global Correlation Functional" G(u20d7S) representing the expected overlap between a fixed control sequence (strategy)u20d7 S and a random Bernoulli target vector (nature)u20d7 X. By treating the strategyu20d7 S as a gauge degree of freedom, we demonstrate—both analytically and via Monte Carlo simulation—that the expectation value of the overlap is invariant under all local permutations ofu20d7 S. We conclude that in memoryless systems, the derivative of success with respect to strategy is identically zero(∇u20d7 S G = 0), implying that all strategies are microcanonically equivalent. This framework offers a pedagogical bridge between classical probability and the concept of gauge invariance in theoretical physics.
Category: Mathematical Physics
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