Nonperturbative results for the mass dependence of the QED fermion determinant

TL;DR

This paper investigates the nonperturbative mass dependence of the QED fermion determinant in symmetric background fields, revealing the anomaly's role and identifying specific mass values where interactions effectively vanish.

Contribution

It demonstrates that the anomaly determines the leading mass singularity and identifies conditions where the nonperturbative determinant equals the free case.

Findings

The anomaly fixes the leading mass singularity of the determinant.

There exists at least one fermion mass where the nonperturbative determinant equals the noninteracting value.

The results apply to a broad class of symmetric background gauge fields.

Abstract

The fermion determinant in four-dimensional quantum electrodynamics in the presence of O(2)XO(3) symmetric background gauge fields with a nonvanishing global chiral anomaly is considered. It is shown that the leading mass singularity of the determinant's nonperturbative part is fixed by the anomaly. It is also shown that for a large class of such fields there is at least one value of the fermion mass at which the determinant's nonperturbative part reduces to its noninteracting value.