Pfaff systems theory and the unifications of gravitation and electromagnetism

TL;DR

This paper employs Pfaff systems theory to analyze differential equations related to conformal and Poincaré Lie equations, deriving electromagnetic and gravitational potentials and their interaction fields, offering new insights into unifying these fundamental forces.

Contribution

It introduces a novel application of Pfaff systems theory to unify gravitation and electromagnetism through differential equations and physical interpretations of potentials.

Findings

Derived differential equations for interaction fields.

Identified physical meanings for infinitesimal variations.

Proposed possible physical interpretations of the unification.

Abstract

We show in the framework of Pfaff systems theory, the functional dependences of the general analytic solutions of a suitable system of involutive differential equations describing the differences between the analytic solutions of the conformal and "Poincar\'e" Lie equations. Then we ascribe to the infinitesimal variations of the parametrizing functionals some physical meanings as the electromagnetic and gravitation potentials. We also deduce their corresponding fields of interactions together with the differential equations they must satisfy. Then we discuss on various possible physical interpretations.