Frobenius curvature, electromagnetic strain and description of photon-like objects

TLDR: In this paper, a general idea for describing 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, is presented.

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.