From the BRST invariant Hamiltonian to the Field-Antifield Formalism

TL;DR

This paper establishes a formal connection between the Hamiltonian BRST invariant phase space approach and the Lagrangian field-antifield formalism, demonstrating their equivalence for certain gauge theories.

Contribution

It provides a deductive proof of the equivalence between phase space and Lagrangian formalisms in gauge theories starting from the BV unitarized action.

Findings

Proves the equivalence of phase space and Lagrangian formalisms for irreducible first rank theories.

Shows the consistency of the two formalisms in the context of gauge theories.

Clarifies the relationship between different quantization approaches for gauge systems.

Abstract

We study the relation between the lagrangian field-antifield formalism and the BRST invariant phase space formulation of gauge theories. Starting from the Batalin-Fradkin-Vilkovisky unitarized action, we demonstrate in a deductive way the equivalence of the phase space, and the lagrangian field-antifield partition functions for the case of irreducible first rank theories.