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.