  Covariant (polysymplectic)Hamiltonian field theory is the Hamiltonian
counterpart of classical Lagrangian field theory. They are quasi-equivalent in
the case of almost-regular Lagrangians. This work addresses BV quantization of
polysymplectic Hamiltonian field theory. We compare BV quantizations of
associated Lagrangian and polysymplectic Hamiltonian field systems in the case
of almost-regular quadratic Lagrangians.
