Variational tricomplex of a local gauge system, Lagrange structure and weak Poisson bracket

TL;DR

This paper introduces a variational tricomplex framework applicable to gauge systems, establishing a link between Lagrangian and Hamiltonian formalisms and enabling construction of weak Poisson structures and BRST charges.

Contribution

It develops the concept of a variational tricomplex with symplectic structure, providing a covariant method to connect Lagrangian and Hamiltonian descriptions of gauge systems.

Findings

Constructed the generating functional of weak Poisson structure from Lagrange structure.

Proposed a covariant procedure for deriving the classical BRST charge from BV master action.

Illustrated the approach with Maxwell's electrodynamics and chiral bosons.

Abstract

We introduce the concept of a variational tricomplex, which is applicable both to variational and non-variational gauge systems. Assigning this tricomplex with an appropriate symplectic structure and a Cauchy foliation, we establish a general correspondence between the Lagrangian and Hamiltonian pictures of one and the same (not necessarily variational) dynamics. In practical terms, this correspondence allows one to construct the generating functional of weak Poisson structure starting from that of Lagrange structure. As a byproduct, a covariant procedure is proposed for deriving the classical BRST charge of the BFV formalism by a given BV master action. The general approach is illustrated by the examples of Maxwell's electrodynamics and chiral bosons in two dimensions.