Residual gauge symmetry in light-cone electromagnetism

TL;DR

This paper investigates the residual gauge symmetries in light-cone electromagnetism, relaxing boundary conditions to identify all gauge transformations and analyzing their implications for the theory's structure and radiation fields.

Contribution

It introduces a comprehensive analysis of residual gauge transformations in light-cone electromagnetism by relaxing boundary conditions and computing canonical generators.

Findings

Identified all residual gauge transformations including large gauge transformations.

Distinguished between trivial and large gauge transformations in light-cone electromagnetism.

Analyzed the structure of light-cone Hamiltonians and radiation fields using Newman-Penrose formalism.

Abstract

We analyze the residual gauge freedom in light-cone electromagnetism in four dimensions. The standard boundary conditions involved in the so-called $lc_2$ formalism, which contains only the two physical degrees of freedom, allow for a subset of residual gauge transformations. We relax the boundary conditions imposed on the fields in order to obtain all the residual gauge transformations. We compute the canonical generators for Poincar\'e and gauge transformations with these relaxed boundary conditions. This enables us to distinguish between the trivial (proper) and large (improper) gauge transformations in light-cone electromagnetism. We then employ the Newman-Penrose formalism to identify the incoming and outgoing radiation fields. We comment on the quadratic form structure of light-cone Hamiltonians, often encountered in $lc_2$ gauge theories.