Mathematical Physics

Deformed Lie Products in a 4D Space Isotropic Electromagnetic Fields

Authors: Thierry L. A. Periat
Comments: 44 Pages. In the French language

In a previous work, the simplest decomposition without residual part of a generic deformed Lie product f has been interpreted as the representation of a (2, 0) version of some EM field in M(4, C). This document (in the French language) is precising the conditions of validity for this interpretation. It proves: (i) that isotropic EM fields are compatible with it; (ii) again, the existence of Lie algebras; (iii) that the passage between the simplest decomposition of f and the antisymmetric decomposition of (f o f) (both without residual part) is an EM transition involving isotropic EM fields presumably linked with natural electromagnetic oscillations in Maxwell's vacuum. Since their effective nature remains to be identified, one is pushed to propose a new interpretation for f involving the dual representation of any EM field.Key words: representations of the EM fields, Lie algebras, evolution.
Category: Mathematical Physics

The Natural Velocity of Bodies in the Tensional Field of the Vacuum

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 14 Pages. (Note by viXra Admin: For the last time, please refrain from repeated submissions and cancellations and SUBMIT article written with AI assistance to ai.viXra.org)

In traditional models, gravity is treated either as a force between masses or as the curvature of spacetime induced by energy. In the Principium Geometricum, we propose a different reading:Force does not act on mass, but on volume; and the response of the tense vacuum to the presence of a body manifests as a natural velocity, measurable through geometry. The vacuum field is endowed with a tensional structure. Bodies inserted into this field deform its geometry, and the field responds by providing a displacement velocity proportional to the geometric disturbance. This velocity is not the result of external force, but a natural expression of the medium’s internal resistance.
Category: Mathematical Physics

A Dimensional Identity Connecting Gravity and Electromagnetism via the Fine-Structure Constant

Authors: Jonathan Loomis
Comments: 4 Pages.

We present a dimensional identity that connects the gravitational constant, the fine-structure constant, the vacuum permittivity, and the Planck mass. While not predictive on its own, this identity suggests a potential structuralrelationship between gravitational and electromagnetic constants. The formulation allowsG to be expressed in terms of electromagnetic parameters and a mass scale equal to the Planck mass, offering a concise and dimensionally exact connection between domains typically treated as distinct. Though speculative, the precision and dimensional consistency of this identity motivate further scrutiny.
Category: Mathematical Physics

Gravity as Toroidal Geometry of Time: Reformulating Einstein with Angular Tension

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 4 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

Wepropose a reformulation of Einstein’s field equations based on the concept of a time-tensional toroidal geometry. The unification constant αU = ApKe replaces Newtonian mass as the source of curvature. We define a tension-based vector field Uµ, from which we construct a geometric energy-momentum tensor T µν, and derive a new class of field equations. We show that in the weak-field limit, this formulation recovers Newtonian gravity, while offering a deeper ontological interpretation of space, time, and matter.
Category: Mathematical Physics

Involutive Lie Products in Four-Dimensional Spaces (Les Produits de Lie Involutifs Dans Les Espaces de Dimension Quatre)

Authors: Thierry L. A. Periat
Comments: 32 Pages. In French

This document is the French version of the reference: "Deformed Lie Products and Involution - Second part: in a Four-dimensional Space; viXra:2507.0062, 40 pages". The progression follows a similar way of thinking. But it goes a step further because it can clearly connect a family of deformed Lie products with specific representations of the electromagnetic fields. The conditions precising the existence of an involution are also better explained.

Ce document explore, dans un espace mathématique de dimension quatre, les notions d'invariance et d'involution lorsque celles-ci s'appliquent à l'action d'un produit de Lie déformé. Il rappelle l'existence de la décomposition sans résidu la plus simple rencontrée au cours des explorations précédentes. Mais il démontre aussi l'existence d'une autre décomposition sans résidu en se servant de la multiplicité des représentations du produit de Lie déformé. Il définit les conditions assurant l'égalité des deux décompositions. Aucune des deux matrices ne peut assurer l'invariance et seule la décomposition la plus simple permet d'envisager une action de type involutive. Enfin, il établit clairement les relations faisant de la décomposition la plus simple une représentation effective d'un champ électromagnétique.
Category: Mathematical Physics

On the Calculation of Both Power and Moment Required of Motors to Drive a Robot Arm in a Controllable Manner

Authors: Aloys J. Sipers, Joh. J. Sauren
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific references)

In this letter we use complex numbers to calculate both the power and the mechanical moment required of robot motors to drive a robot arm subjected to loads on joints and on multiple parts.
Category: Mathematical Physics

An Algebraic Derivation to Determine Lorentzian Broadening from Voigt Function in Plasma Diagnostics

Authors: Zi-Jing Chiah, Elton Song-Zhe Mah
Comments: 3 Pages.

This paper presents an algebraic derivation to express Lorentzian broadening, as a function of the Voigt, and Gaussian widths, providing a practical method for extracting electron density from spectroscopic data in plasma diagnostics.
Category: Mathematical Physics

Principium Geometricum II: How the Minimum Space Tension Reveals the Gravastar-Like Black Hole

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 41 Pages. In Portuguese

We present the Principium Geometricum, a new unified theoretical framework that emerges from three classical pillars—Newton's Second Law, Gauss's Law, and Einstein's Equations. We propose a fundamental vector field Uμ, whose divergence defines geometric mass and whose temporal oscillation modulates the spacetime metric. We introduce the unifying constant αU = keℓ2 P , of dimension force × area, which allows us to recover the four fundamental interactions in a single formalism. From a Lagrangian constructed for the field Uμ, we derive the energy-momentum tensor Tμν , derive its quantization, calculate the vacuum energy and propose mixed interactions with the electromagnetic field. The results point to a profound reshaping of the structure of spacetime as a field of pulsating areas, paving the way for the geometric unification of classical, relativistic and quantum physics.
Category: Mathematical Physics