BV quantization of covariant (polysymplectic) Hamiltonian field theory

TL;DR

This paper explores the BV quantization process for covariant polysymplectic Hamiltonian field theory, comparing it with Lagrangian systems, especially for almost-regular quadratic Lagrangians, to deepen understanding of quantum field formulations.

Contribution

It provides a comparison of BV quantizations between Lagrangian and Hamiltonian formulations in covariant field theory for almost-regular quadratic Lagrangians, highlighting their quasi-equivalence.

Findings

BV quantization of Hamiltonian field theory is developed.

Comparison shows quasi-equivalence with Lagrangian systems.

Results facilitate understanding of quantum formulations in covariant field theories.

Abstract

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.