Gauge-invariant Green function in 3+1 dimensional QED (QCD) and 2+1 dimensional Abelian (Non-Abelian) Chern-Simon theory

TL;DR

This paper develops a method to analyze gauge-invariant fermion Green functions across different dimensions and gauge theories, with implications for quantum Hall systems.

Contribution

It extends a simple method for gauge-invariant Green functions from 2+1D QED to 3+1D QED and 2+1D Chern-Simons theories, including non-Abelian cases.

Findings

Method successfully applied to various gauge theories.

Results suggest relevance to Fractional Quantum Hall effect.

Provides a unified approach to gauge-invariant Green functions.

Abstract

By applying the simple and effective method developed to study the the gauge-invariant fermion Green function in $ 2+1 $ dimensional non-compact QED, we study the gauge-invariant Green function in $ 3+1 $ dimensional QED and $ 2+1 $ dimensional non-compact Chern-Simon theory. We also extend our results to the corresponding $ SU(M) $ non-Abelian gauge theories. Implications for Fractional Quantum Hall effect are briefly discussed.