Hamiltonian BRST and Batalin-Vilkovisky formalisms for second quantization of gauge theories

TL;DR

This paper explores the Hamiltonian BRST and Batalin-Vilkovisky formalisms for the second quantization of gauge theories, providing a foundational approach to quantizing gauge systems with different symmetries.

Contribution

It constructs the proper solution of the classical BV master equation from first principles within the Hamiltonian BRST framework, linking it to standard master actions.

Findings

Proper BV solutions derived from Hamiltonian BRST formalism

Connection established between time reparametrization invariance and standard master actions

Framework applicable for second quantization of gauge theories

Abstract

Gauge theories that have been first quantized using the Hamiltonian BRST operator formalism are described as classical Hamiltonian BRST systems with a BRST charge of the form <\Psi,\Omega\Psi>_{even} and with natural ghost and parity degrees for all fields. The associated proper solution of the classical Batalin-Vilkovisky master equation is constructed from first principles. Both of these formulations can be used as starting points for second quantization. In the case of time reparametrization invariant systems, the relation to the standard <\Psi,\Omega\Psi>_{odd} master action is established.