Hamiltonian Dynamics for an alternative action describing Maxwell's equations

TL;DR

This paper performs a detailed Hamiltonian analysis of an alternative action for Maxwell's equations, revealing it lacks gauge symmetry and differs in physical degrees of freedom from standard Maxwell theory.

Contribution

It provides a complete Dirac's canonical analysis of an alternative Maxwell action, highlighting differences in symmetries and degrees of freedom compared to the standard theory.

Findings

The alternative action does not possess gauge symmetry.

The number of physical degrees of freedom differs from Maxwell's theory.

The analysis clarifies the symmetry structure of the alternative model.

Abstract

We develop a complete Dirac's canonical analysis for an alternative action that yields Maxwell's four-dimensional equations of motion. We study in detail the full symmetries of the action by following all steps of Dirac's method in order to obtain a detailed description of symmetries. Our results indicate that such an action does not have the same symmetries than Maxwell theory, namely, the model is not a gauge theory and the number of physical degrees of freedom are different.