Debye Potentials for Maxwell and Dirac Fields from a Generalisation of the Killing-Yano Equation

TL;DR

This paper introduces a method to derive scalar potentials for Maxwell and Dirac fields using conformal Killing-Yano tensors, and constructs symmetry operators that generate new solutions from existing ones.

Contribution

It presents a novel approach to obtain scalar potentials and symmetry operators for Maxwell and Dirac equations via conformal Killing-Yano tensors.

Findings

Scalar potentials for Maxwell and Dirac fields derived

Symmetry operators constructed from conformal Killing-Yano tensors

Method enhances solution-generating techniques for these fields

Abstract

By using conformal Killing-Yano tensors, and their generalisations, we obtain scalar potentials for both the source-free Maxwell and massless Dirac equations. For each of these equations we construct, from conformal Killing-Yano tensors, symmetry operators that map any solution to another.