Hamiltonian Analysis of an On-shell U(1) Gauge Field Theory

TL;DR

This paper performs a Hamiltonian analysis of an on-shell U(1) gauge theory, revealing it has only two photon polarizations and is free of ghosts at the classical level despite explicit symmetry breaking.

Contribution

It provides a Hamiltonian formulation of an on-shell U(1) gauge theory, showing the constraints and physical degrees of freedom without standard gauge invariance.

Findings

Photon polarizations are limited to two at the classical level.

The reduced Hamiltonian is bounded from below.

The theory is ghost-free at the classical level.

Abstract

We perform the Hamiltonian analysis of an on-shell U(1) gauge field theory, in which the action is not invariant under local U(1) transformations but recovers the invariance when the equations of motion are imposed. We firstly apply Dirac's method of Hamiltonian analysis. We find one first-class constraint and two second-class constraints in the vector sector. It implies the photons have only two polarisations, at least at the classical level, although the standard U(1) symmetry is explicitly broken. The reduced Hamiltonian is bounded from below and the on-shell U(1) gauge field theory is free from ghosts at the classical level.