Unification of massless field equations solutions for any spin

¹ Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez - Santiago 7491169, Chile
² Departamento de Física, Facultad de Ciencias, Universidad de Chile - Santiago 7800003, Chile
³ Centro de Recursos Educativos Avanzados, CREA - Santiago 7500018, Chile
⁴ Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez - Santiago 7491169, Chile

^(a) E-mail: sergio.hojman@uai.cl
^(b) E-mail: felipe.asenjo@uai.cl (corresponding author)

Received: 24 November 2021
Accepted: 23 December 2021

Abstract

A unification in terms of exact solutions for massless Klein-Gordon, Dirac, Maxwell, Rarita-Schwinger, Einstein, and bosonic and fermionic fields of any spin 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 the d'Alembert 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 exact non-trivial solutions to Klein-Gordon, Dirac, Maxwell, Rarita-Schwinger, (linearized and full) Einstein and any spin bosonic and fermionic field 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.