BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on Fock space

TL;DR

This paper presents a Hamiltonian-based BRST quantization method for Yang-Mills theories, introducing a new ghost field representation and constructing a Hamiltonian that reproduces classical equations quantum mechanically.

Contribution

It offers a purely Hamiltonian approach to BRST quantization of Yang-Mills theories, with a novel ghost field representation and a Hamiltonian that captures classical dynamics.

Findings

New ghost field representation with self-adjointness and canonical anticommutation

Constructed a minimal BRST invariant Hamiltonian for Yang-Mills

Hamiltonian evolution reproduces classical Yang-Mills equations

Abstract

We develop the basic ideas and equations for the BRST quantization of Yang-Mills theories in an explicit Hamiltonian approach, without any reference to the Lagrangian approach at any stage of the development. We present a new representation of ghost fields that combines desirable self-adjointness properties with canonical anticommutation relations for ghost creation and annihilation operators, thus enabling us to characterize the physical states on a well-defined Fock space. The Hamiltonian is constructed by piecing together simple BRST invariant operators to obtain a minimal invariant extension of the free theory. It is verified that the evolution equations implied by the resulting minimal Hamiltonian provide a quantum version of the classical Yang-Mills equations. The modifications and requirements for the inclusion of matter are discussed in detail.