Peierls Brackets in Theoretical Physics

TL;DR

This paper introduces Peierls brackets, a group-invariant Poisson bracket useful in quantum field theory and general relativity, emphasizing their theoretical foundation and applications.

Contribution

It provides an introductory overview of Peierls brackets, highlighting their construction, properties, and relevance to field theory and diffeomorphism invariance.

Findings

Peierls brackets are group-invariant Poisson brackets.

They are well suited for use with the full diffeomorphism group.

Applications to field theory and point Lagrangians 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 field theory and point Lagrangians.