Classical electrodynamics and gauge symmetry of the X-boson

Abstract

The classical electrodynamics for X-boson model is studied to understand it propagation in the space–time. The Maxwell equations of model and the correspondents wave equations are obtained. It indicate the dispersion relations of a massive and massless particle, that we interpret as photon and the X-boson. Thereby, a full diagonalization of the model is introduced to get a Maxwell sector summed up to Proca sector. Posteriorly, the X-fields and X-potentials of a relativistically moving charge is obtained in terms of a time-proper integral, and as an example, we calculate the fields and potentials for a charge in uniform moving. Finally, the gauge symmetry and gauge transformations were discussed.