A note on generalized electrodynamics

TL;DR

This paper explores a generalized form of electrodynamics using matrix equations, analyzing gauge invariance, energy-momentum tensors, and dilatation symmetry, including solutions in curved spacetime backgrounds.

Contribution

It introduces a matrix formulation of generalized Maxwell equations with arbitrary gauge parameters and studies their symmetry properties and solutions in curved spacetime.

Findings

Gauge invariance is broken by a scalar field.

Dilatation symmetry is demonstrated in the model.

Solutions for vector fields in Friedmann-Robertson-Walker background are obtained.

Abstract

The generalized Maxwell equations with arbitrary gauge parameter are considered in the $11\times 11$-matrix form. The gauge invariance of such a model is broken due to the presence of a scalar field. The canonical and symmetrical Belinfante energy-momentum tensors are found. The dilatation current is obtained and we demonstrate that the theory possesses the dilatation symmetry. The matrix Schr\"{o}dinger form of equations is derived. The non-minimal interaction in curved space-time is introduced and equations are considered in Friedmann - Robertson - Walker background. We obtain some solutions of equations for the vector field.