Frobenius Curvature, Electromagnetic Strain and Description of Photon-like Objects

TL;DR

This paper introduces a novel mathematical framework using Frobenius integrability concepts and electromagnetic strain to describe finite, photon-like physical objects with complex translational-rotational dynamics.

Contribution

It presents a new approach to modeling photon-like objects through nonintegrable distributions and their curvatures, linking geometric structures with physical energy-momentum interactions.

Findings

Defines photon-like objects within a geometric framework.

Uses Frobenius nonintegrability to model energy exchange.

Provides a Lagrangian description of these objects.

Abstract

This paper aims to present a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and structures connected with the Frobenius integrability/nonintegrability theorems and electromagnetic strain quantities. The idea is based on consideration of {\it nonintegrable} subdistributions of some appropriate completely integrable distribution (differential system) on a manifold and then to make use of the corresponding curvatures and correspondingly directed strains as measures of interaction, i.e. of energy-momentum exchange among the physical subsystems mathematically represented by the nonintegrable subdistributions. The concept of photon-like object is introduced and description (including lagrangian) of such objects in these terms is given.