Causality and Peierls Bracket in Classical Mechanics

TL;DR

This paper explores the relationship between Peierls brackets and Poisson brackets in classical mechanics, especially in time-dependent systems, highlighting their equivalence in simple cases and the need for a general proof.

Contribution

It derives the relation between Peierls and Poisson brackets in classical mechanics, clarifying their connection in time-dependent systems.

Findings

Equal-time Peierls brackets match Poisson brackets in simple cases

A proof for the equivalence in general Hamiltonian systems is still needed

Highlights the importance of Peierls brackets in classical mechanics

Abstract

Relation between the Peierls and the Poisson bracket is derived in classical mechanics of time-dependent systems. Equal-time Peierls brackets are seen to be the same as the Poisson brackets in simple cases but a proof for a general Hamiltonian is lacking.