Nonlinear Connections and Description of Photon-like Objects

TL;DR

This paper introduces a mathematical framework using nonintegrable distributions and curvature to describe finite photon-like objects with complex translational-rotational dynamics and energy interactions.

Contribution

It presents a novel approach to modeling photon-like objects through nonintegrable distributions and curvature, capturing their finite spatial structure and internal energy exchange.

Findings

Photon-like objects are modeled as nonintegrable distributions.

Curvature measures are used to quantify energy-momentum exchange.

The framework provides a geometric description of finite, dynamic photon-like entities.

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 given in terms of distributions on manifolds with corresponding curvature defined by the Nijenhuis operator. 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 as generators of 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 of such objects in these terms is given.