On First-Order Generalized Maxwell Equations

TL;DR

This paper extends Maxwell's equations by incorporating a scalar field in a first-order formalism, analyzing gauge invariance breaking, energy-momentum tensors, and performing canonical quantization to derive the field propagator.

Contribution

It introduces a first-order formalism for generalized Maxwell equations with a scalar field, exploring gauge invariance breaking and quantization methods.

Findings

Gauge invariance is broken, leading to a scalar field.

Energy-momentum tensors have non-zero traces, indicating broken dilatation symmetry.

Canonical quantization yields the field propagator in the first-order formalism.

Abstract

The generalized Maxwell equations including an additional scalar field are considered in the first-order formalism. The gauge invariance of the Lagrangian and equations is broken resulting the appearance of a scalar field. We find the canonical and symmetrical Belinfante energy-momentum tensors. It is shown that the traces of the energy-momentum tensors are not equal to zero and the dilatation symmetry is broken in the theory considered. The matrix Hamiltonian form of equations is obtained after the exclusion of the nondynamical components. The canonical quantization is performed and the propagator of the fields is found in the first-order formalism.