Unification of massless field equations solutions for any spin

TL;DR

This paper presents a unified method to derive exact solutions for all massless field equations of any spin by expressing fields through pre-potentials satisfying the wave equation, unifying solutions across different theories.

Contribution

It introduces a novel approach using pre-potentials to unify solutions of massless field equations for any spin, including Einstein's equations, in a single framework.

Findings

Exact solutions for massless fields of any spin are constructed.

Pre-potentials satisfying the wave equation generate solutions for various field equations.

The method links to previous approaches and broadens understanding of massless field solutions.

Abstract

A unification of Klein--Gordon, Dirac, Maxwell, Rarita--Schwinger and Einstein equations exact solutions (for the massless fields cases) is presented. The method is based on writing all of the relevant dynamical fields in terms of products and derivatives of pre--potential functions, which satisfy d'Alambert equation. The coupled equations satisfied by the pre--potentials are non-linear. Remarkably, there are particular solutions of (gradient) orthogonal pre--potentials that satisfy the usual wave equation which may be used to construct {\it{exact non--trivial solutions to Klein--Gordon, Dirac, Maxwell, Rarita--Schwinger and (linearized and full) Einstein equations}}, thus giving rise to a unification of the solutions of all massless field equations for any spin. Some solutions written in terms of orthogonal pre--potentials are presented. Relations of this method to previously developed ones, as well as to other subjects in physics are pointed out.