Koszul-Tate Cohomology For an Sp(2)-Covariant Quantization of Gauge Theories with Linearly Dependent Generators

TL;DR

This paper extends the BV quantization method to include Sp(2)-covariance for reducible gauge theories by utilizing Koszul-Tate cohomology, ensuring a consistent and equivalent quantization framework.

Contribution

It introduces a novel implementation of Sp(2)-covariant quantization using Koszul-Tate cohomology without duplicating gauge symmetries, demonstrating equivalence with BLT quantization.

Findings

Successful implementation of Sp(2)-covariant quantization in BV framework

Proof of equivalence between Sp(2)-covariant and BLT quantizations

Establishment of acyclicity of Koszul-Tate differential in this context

Abstract

The anti-BRST transformation, in its Sp(2)-symmetric version, for the general case of any stage-reducible gauge theories is implemented in the usual BV approach. This task is accomplished not by duplicating the gauge symmetries but rather by duplicating all fields and antifields of the theory and by imposing the acyclicity of the Koszul-Tate differential. In this way the Sp(2)-covariant quantization can be realised in the standard BV approach and its equivalence with BLT quantization can be proven by a special gauge fixing procedure.