Surface charge algebra in gauge theories and thermodynamic integrability

TL;DR

This paper explores the algebra of surface charges in gauge theories, analyzing their integrability and algebraic structure, especially at asymptotic boundaries, and connects various formalisms to understand their properties.

Contribution

It provides a unified covariant derivation of surface charge algebra, including central extensions, and clarifies the role of integrability and different formalisms in gauge theories.

Findings

Surface charges form a Pfaff system in exact solutions.

Charges associated with symmetry algebra vanish in certain cases.

Asymptotic charges can be centrally extended, affecting algebra representations.

Abstract

Surface charges and their algebra in interacting Lagrangian gauge field theories are investigated by using techniques from the variational calculus. In the case of exact solutions and symmetries, the surface charges are interpreted as a Pfaff system. Integrability is governed by Frobenius' theorem and the charges associated with the derived symmetry algebra are shown to vanish. In the asymptotic context, we provide a generalized covariant derivation of the result that the representation of the asymptotic symmetry algebra through charges may be centrally extended. Finally, we make contact with Hamiltonian and with covariant phase space methods.