Field operators in topological quantum theories

TL;DR

This paper develops a canonical quantization framework for Chern-Simons topological quantum field theories in R^3, demonstrating equivalence between path-integral and operator formalisms and deriving the one-loop effective action.

Contribution

It introduces a Fock space representation for free field operators in Chern-Simons theories and establishes their perturbative equivalence with the path-integral approach.

Findings

Fock space representation of field operators derived

Perturbative equivalence between formalisms shown

One-loop effective action explicitly computed

Abstract

The perturbative approach to the topological quantum field theories of the Chern-Simons type formulated in R^3 is considered. By means of the canonical quantization of the euclidean Chern-Simons lagrangian in the Landau gauge, a Fock space representation of the free field operators is produced. The perturbative equivalence of the path-integral formalism and the field operator approach is exhibited. The expression of the one-loop effective action in background gauge is derived.