Classical electrodynamics and gauge symmetry of the X-boson

TL;DR

This paper explores the classical electrodynamics and gauge symmetry of the X-boson, a candidate dark matter particle, deriving wave equations, dispersion relations, and analyzing charge motion within the model.

Contribution

It introduces a detailed classical electrodynamics framework for the X-boson, including gauge symmetry, wave equations, and a full model diagonalization separating Maxwell and Proca sectors.

Findings

Derived Maxwell-type and wave equations for the X-boson.

Identified dispersion relations for massive and massless particles.

Analyzed charge motion and electromagnetic potentials for the X-boson.

Abstract

In this paper we have obtained several new results concerning the X-boson, which is being considered recently as one of the main candidate of the dark matter particle content. The classical electrodynamics for the X-boson model was explored to understand its propagation in space-time. The field equations (Maxwell-type) and the corresponding wave equations were obtained. They indicate the dispersion relations of both a massive and massless particles. These results can be interpreted as a photon and the X-boson (with a mass of 17 MeV), respectively. The gauge symmetry and gauge transformations were discussed. A full model diagonalization was introduced to obtain a Maxwell sector added up to a Proca sector. After that, we have obtained the retarded Green functions which yield the inhomogeneous solutions of the wave equations for the X-boson fields. We have applied this solution to the charge point motion, and we transformed the potential solution to a quadrature problem. In particular, as an example, we have analyzed the point charge in a straight line uniform motion, where the corresponding electromagnetic charge were calculated.