Phase of the fermion determinant in QED_3 using a gauge invariant lattice regularization

TL;DR

This paper investigates the phase of the fermion determinant in three-dimensional QED using a gauge-invariant lattice approach, revealing insights into parity anomalies and non-perturbative effects in various gauge backgrounds.

Contribution

It introduces a canonical formalism to analyze the fermion determinant's phase in different gauge backgrounds, highlighting the role of free fermion propagation in parity anomalies.

Findings

Identifies a phase responsible for the parity anomaly in electric flux backgrounds.

Analyzes the structure of parity-breaking perturbative terms at finite temperature and mass.

Provides a gauge-invariant lattice framework for non-perturbative study of fermion determinants.

Abstract

We use canonical formalism to study the fermion determinant in different three dimensional abelian gauge field backgrounds that contain non-zero magnetic and electric flux in order to understand the non-perturbative contributions to the parity-odd and parity-even parts of the phase. We show that a certain phase associated with free fermion propagation along a closed path in a momentum torus is responsible for the parity anomaly in a background with non-zero electric flux. We consider perturbations around backgrounds with non-zero magnetic flux to understand the structure of the parity-breaking perturbative term at finite temperature and mass.