ON THE BV QUANTIZATION OF GAUGE GRAVITATION THEORY

Quantization of gravitation theory as gauge theory of general covariant transformations in the framework of Batalin–Vilkoviski (BV) formalism is considered. Its gauge-fixed Lagrangian is constructed.

BV QUANTIZATION OF COVARIANT (POLYSYMPLECTIC) HAMILTONIAN FIELD THEORY

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 Batalin–Vilkoviski (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.

AXIAL ANOMALY FROM THE BPHZ RENORMALIZED BV MASTER EQUATION

We show here that a rigid anomaly (anomalous divergence of a classically conserved Noether current) can also be calculated using the BPHZ renormalized form of the master equation of the field antifield (or BV) quantization. Considering the case of QED (where there is no gauge anomaly), the fundamental result about the anomalous contribution to the axial Ward identity is reproduced in this BPHZ regularized BV framework (originally used to compute gauge anomalies).

ON THE PERTURBATIVE EQUIVALENCE BETWEEN THE HAMILTONIAN AND LAGRANGIAN QUANTIZATIONS

The Hamiltonian (BFV) and Lagrangian (BV) quantization schemes are proved to be perturbatively equivalent to each other. It is shown in particular that the quantum master equation being treated perturbatively possesses a local formal solution.

BV QUANTIZATION OF A VECTOR-TENSOR GAUGE THEORY WITH TOPOLOGICAL COUPLING

We use the BV quantization method for a theory with coupled tensor and vector gauge fields through a topological term. We consider in detail the reducibility of the tensorial sector as well as the appearance of a mass term in the effective vectorial theory.

A NOTE ON ABELIAN CONVERSION OF CONSTRAINTS

We show that for a system containing a set of general second class constraints which are linear in the phase space variables, the Abelian conversion can be obtained in a closed form and that the first class constraints generate a generalized shift symmetry. We study in detail the example of a general first order Lagrangian and show how the shift symmetry noted in the context of BV quantization arises.