BRST quantization of matrix models with constraints and two-dimensional Yang-Mills theory on the cylinder

TL;DR

This paper applies BRST quantization to a constrained matrix model representing 2D Yang-Mills theory on a cylinder, constructing generators and Hamiltonians, and comparing it to the reduced phase space approach.

Contribution

It introduces a BRST quantization framework for the matrix model of 2D Yang-Mills theory, providing explicit constructions and discussing advantages over traditional methods.

Findings

BRST generators and Hamiltonians are explicitly constructed.

Evolution operator is expressed via BRST path integral.

Advantages over reduced phase space approach are discussed.

Abstract

BRST quantization of the one-dimensional constrained matrix model which describes two-dimensional Yang-Mills theory on the cylinder is performed. Classical and quantum BRST generators and BRST-invariant hamiltonians are constructed. Evolution operator is expressed in terms of BRST path integral. Advantages of the BRST quantization over the reduced phase space approach leading to the theory of $N$ free fermions are discussed.