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| viXra.org > Mathematical Physics > 2505 |
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[7] viXra:2505.0174 [pdf] submitted on 2025-05-26 04:03:55
Authors: Chenjia Li, Jingxu Wu
Comments: 15 Pages.
The theory of tensors and pseudotensors underlies the mathematical framework of modern physics, providing a coordinate-invariant language for describing physical laws and symmetries. In this work, we systematically analyze the transformationproperties of tensors and pseudotensors of various ranks, with particular emphasis on their behavior under spatial and spacetime reflections. The construction and interpretation of the Levi-Civita symbol in two, three, and four dimensionsare discussed in detail, elucidating the essential distinction between true tensors and pseudotensors in terms of orientation and parity. Explicit transformation rules for ordinary tensors and pseudotensors are derived, including the role of the Jacobian determinant and its sign. Through concrete examples—including scalar tripleproducts, cross products, and antisymmetric tensor decompositions—we reveal the fundamental algebraic and geometric features of these mathematical objects. The implications for vector calculus, relativistic field theory, and physical invariants such as chirality and duality are highlighted. Our results provide a unified and rigoroustreatment of the reflection and contraction properties of pseudotensors, with direct relevance to applications in classical mechanics, electromagnetism, and modern theoretical physics.
Category: Mathematical Physics
[6] viXra:2505.0072 [pdf] submitted on 2025-05-12 18:30:56
Authors: Józef Radomański
Comments: Pages.
The book is a completely new and unconventional look at selected problems of classical physics and is intended for people interested in Special Relativity and relativistic electrodynamics. The idea of Special Relativity is based on the invariance of the laws of physics under the transformations belonging to the Lorentz group. These transformations are internal in real space-time. The author found a complex linear transformation that maintains the invariance of the wave equation but requires the complex domain. The results of the research on this transformation are presented in this monograph. For the research, the author constructed a simple mathematical tool equivalent to Geometric Algebra based on the formalism of the well-known matrix calculus. Although the considerations are carried out in full accordance with the postulates of the classical SR, the use of the paravector calculus to describe the basic laws of physics resulted in surprising results. However, this does not mean that these results contradict experiments. The monograph explains how and why complex phenomena are visible to the observer as real. Finally, an outline of the mathematical structure of complex space-time is presented, which is definitely different from Minkowski space.
Category: Mathematical Physics
[5] viXra:2505.0064 [pdf] submitted on 2025-05-10 20:34:33
Authors: Faysal EL Khettabi
Comments: 9 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This report outlines a foundational shift in mathematics, proposing a framework groundedin finite, constructive principles—the "Arithmetic of Order"—emerging from the progression 1 → n → n + 1 and the combinatorial structure of powersets P(Ωn). It critiques the traditional reliance on infinitary constructs like the complex number i ∈ C and the continuumfor describing physical systems with finite degrees of freedom. Instead, it posits characteristic functions as the true empirical interface, and demonstrates how optimal mathematical structures—such as the Golay code G24, the Leech lattice Λ24, and the Mathieu group M24—emerge deterministically from this finitistic basis through processes of constraint-guided differentiation. This approach offers a new foundation for understanding hyper-complex numbers, projective geometries emergent from powersets, universal principles of communication and information stability, and the potential architectures for advanced arti-ficial intelligence. Crucially, it reinterprets the continuum not as an *a priori* given, but as an asymptotic limit of the nested powerset hierarchy. The principles underlying theoremslike Gleason’s are viewed not merely as specific results at a particular n (such as n = 24),but as exemplars of universal rules of emergence that guide the formation of order acrossall degrees of freedom. The entire framework operates without recourse to unobservableinfinities or the subjective concept of "noise."
Category: Mathematical Physics
[4] viXra:2505.0056 [pdf] submitted on 2025-05-07 21:29:38
Authors: Alfonso De Miguel bueno
Comments: 4 Pages.
This article proposes a reinterpretation of Lobachevsky’s imaginary geometry as a hyperdimensional, specular structure arising from the intersection of two three-dimensional Euclidean spaces. The model describes non-Euclidean parallelism as emerging dynamically from oscillating curvatures, leading to a topological system with four subspaces, two transverse and two vertical, whose behavior is governed by synchronized or opposing phases.
Category: Mathematical Physics
[3] viXra:2505.0055 [pdf] submitted on 2025-05-07 23:30:42
Authors: Ervin Goldfain
Comments: 6 Pages.
We give a pedagogical account on the origin of fractal spacetime stemming from the Heisenberg uncertainty relations at ultrashort distance scales.
Category: Mathematical Physics
[2] viXra:2505.0042 [pdf] submitted on 2025-05-07 03:18:02
Authors: David B. Graham
Comments: 23 Pages.
In Newtonian physics, it commonly assumed that conservations of linear momentum and angular momentum are independent. This paper shows the gradient of the angular momentum field is populated by components of linear momentum, which allows calculation of linear momentum from a few angular momentum values displaced an arbitrary distance. Therefore conservation of linear momentum is a necessary condition for full conservation of angular momentum (unchanging angular momentum at every (x,y,z), with unchanging gradient).These results are shown to be equally valid under left hand convention.Examples analyzed include a body orbiting in a central force, which has angular momentum changing at every observation point but one, contrasted with actual conservation of angular momentum (unchanging at every observation point, in every frame of reference). Translating angular momentum of the center of mass within and between frames of reference are discussed. A Python script is provided, to conveniently generate and evaluate random groups of particles.
Category: Mathematical Physics
[1] viXra:2505.0003 [pdf] submitted on 2025-05-01 17:22:55
Authors: Thierry L. A. Periat
Comments: 24 Pages.
This document continues the systematic exploration of diverse mathematical methods allowing the decomposition of deformed tensor products. Here, the discussion is focusing attention on deformed Lie products and on conditions generalizing in a four-dimensional mathematical space what has been called the initial theorem during the elaboration of the intrinsic method, the purpose of which was the decomposition of deformed cross products. This mathematical document sheds a particular light on the (2, 0) representations of the electromagnetic fields.
Category: Mathematical Physics
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