Constraints in polysymplectic (covariant) Hamiltonian formalism

In the framework of polysymplectic Hamiltonian formalism, degenerate Lagrangian field systems are described as multi-Hamiltonian systems with Lagrangian constraints. The physically relevant case of degenerate quadratic Lagrangians is analized in detail, and the Koszul–Tate resolution of Lagrangian constraints is constructed in an explicit form. The particular case of Hamiltonian mechanics with time-dependent constraints is studied.