On covariant Poisson brackets in field theory

TL;DR

This paper introduces a general method for constructing covariant Poisson brackets in classical field theory using the concept of Lagrange anchor, extending Peierls' brackets to broader contexts.

Contribution

It presents a novel approach to covariant Poisson brackets in field theory based on Lagrange anchors, applicable to both Lagrangian and non-Lagrangian models.

Findings

Generalized covariant Poisson brackets using Lagrange anchors

Extension of Peierls' bracket to non-Lagrangian systems

Framework applicable to a wide class of classical field theories

Abstract

A general approach is proposed to constructing covariant Poisson brackets in the space of histories of a classical field-theoretical model. The approach is based on the concept of Lagrange anchor, which was originally developed as a tool for path-integral quantization of Lagrangian and non-Lagrangian dynamics. The proposed covariant Poisson brackets generalize the Peierls' bracket construction known in the Lagrangian field theory.