The Koszul-Tate Cohomology in Covariant Hamiltonian Formalism

Abstract

We show that, in the framework of covariant Hamiltonian field theory, a degenerate almost regular quadratic Lagrangian $L$ admits a complete set of non-degenerate Hamiltonian forms such that solutions of the corresponding Hamilton equations, which live in the Lagrangian constraint space, exhaust solutions of the Euler--Lagrange equations for $L$. We obtain the characteristic splittings of the configuration and momentum phase bundles. Due to the corresponding projection operators, the Koszul-Tate resolution of the Lagrangian constraints for a generic almost regular quadratic Lagrangian is constructed in an explicit form.

10 pages, LaTeX

References in corpus (2)

• Generalized Classical BRST Cohomology and Reduction of Poisson Manifolds
• Multimomentum Hamiltonian Formalism in Quantum Field Theory

Cited by in corpus (1)

• Cohomology of the variational complex in BRST theory