Peierls Brackets in Field Theory

TL;DR

This paper introduces Peierls brackets as a group-invariant Poisson bracket framework suitable for quantum field theory and general relativity, emphasizing their application to gauge field theory.

Contribution

It provides an accessible introduction to Peierls brackets and demonstrates their utility in gauge field theory and diffeomorphism-invariant contexts.

Findings

Peierls brackets are group invariant Poisson brackets.

They are well suited for combining Poisson brackets with diffeomorphism groups.

Application examples to gauge field theory are discussed.

Abstract

Peierls brackets are part of the space-time approach to quantum field theory, and provide a Poisson bracket which, being defined for pairs of observables which are group invariant, is group invariant by construction. It is therefore well suited for combining the use of Poisson brackets and the full diffeomorphism group in general relativity. The present paper provides an introduction to the topic, with applications to gauge field theory.