Hamiltonian surface charges using external sources

TL;DR

This paper introduces a method to interpret boundary conditions as external sources, enabling the computation of surface charges in gauge theories with complex boundary conditions within the Hamiltonian framework.

Contribution

It provides a novel approach to handle boundary conditions as external sources, solving the integrability problem in surface charge calculations for gauge symmetries.

Findings

Extended Hamiltonian formalism to include external sources.

Derived surface charges for theories with non-trivial boundary conditions.

Improved understanding of boundary conditions' role in gauge symmetries.

Abstract

In this work, we interpret part of the boundary conditions as external sources in order to solve the integrability problem present in the computation of surface charges associated to gauge symmetries in the hamiltonian formalism. We start by describing the hamiltonian structure of external symmetries preserving the action up to a transformation of the external sources of the theory. We then extend these results to the computation of surface charges for field theories with non-trivial boundary conditions.