Integration measure and extended BRST covariant quantization

TL;DR

This paper introduces an extended BRST invariant Lagrangian quantization framework for gauge theories, utilizing a modified triplectic algebra and supersymplectic structure to ensure a well-defined path integral measure.

Contribution

It develops a new extended BRST quantization scheme based on a modified triplectic algebra, unifying and generalizing existing approaches.

Findings

Provides a consistent measure for the path integral.

Recovers known quantization schemes as special cases.

Establishes a geometric structure underlying the quantization.

Abstract

We propose an extended BRST invariant Lagrangian quantization scheme of general gauge theories based on an explicit realization of the modified triplectic algebra that was announced in our previous investigation (hep-th/0104189). The algebra includes, besides the odd operators $V^a$ appearing in the triplectic formalism, also the odd operators $U^a$ introduced within modified triplectic quantization, both of which being anti-Hamiltonian vector fields. We show that some even supersymplectic structure defined on the space of fields and antifields provides the extended BRST path integral with a well-defined integration measure. All the known Lagrangian quantization schemes based on the extended BRST symmetry are obtained by specifying the (free) parameters of that method.