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

Understand

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.