Covariant Hamiltonian field theory

TL;DR

This paper explores the covariant Hamiltonian formalism in field theory, highlighting gauge fixing in degenerate systems and extending the framework with BRST symmetry to handle gauge invariances.

Contribution

It introduces a BRST extension of covariant Hamiltonian formalism, incorporating gauge fixing and symmetry structures for degenerate field theories.

Findings

Identifies gauge fixing conditions in covariant Hamilton equations for degenerate systems.

Develops a BRST extension with Lie superalgebra of symmetries.

Connects Lagrangian and Hamiltonian formalisms in covariant field theory.

Abstract

We study the relationship between the equations of first order Lagrangian field theory on fiber bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. The main peculiarity of these Hamilton equations lies in the fact that, for degenerate systems, they contain additional gauge fixing conditions. We develop the BRST extension of the covariant Hamiltonian formalism, characterized by a Lie superalgebra of BRST and anti-BRST symmetries.