BRST Quantization of Noncommutative Gauge Theories

TL;DR

This paper develops the BRST quantization framework for noncommutative U(N) gauge theories, demonstrating nilpotency, physical state space characterization, and unitarity of the S-matrix in this context.

Contribution

It introduces the BRST symmetry transformation for noncommutative gauge theories and proves key properties like nilpotency and unitarity, extending the quantization method to noncommutative spaces.

Findings

BRST symmetry is successfully formulated for noncommutative U(N) gauge theories.

The physical state space is characterized by BRST cohomology for space-like non-commutativity.

Unitarity of the S-matrix is established in the physical subspace.

Abstract

In this paper, the BRST symmetry transformation is presented for the noncommutative U(N) gauge theory. The nilpotency of the charge associated to this symmetry is then proved. As a consequence for the space-like non-commutativity parameter, the Hilbert space of physical states is determined by the cohomology space of the BRST operator as in the commutative case. Further, the unitarity of the S-matrix elements projected onto the subspace of physical states is deduced.