Zeta function regularization, anomaly and complex mass term

TL;DR

This paper explores how zeta function regularization handles complex mass terms in fermions, showing it can detect phase information via anomaly equations despite not appearing in the determinant.

Contribution

It demonstrates that zeta function regularization can recognize phase information through anomaly equations even when the fermion determinant lacks the phase.

Findings

Zeta regularization does not show phase in the fermion determinant with complex mass.

Anomaly equations explicitly reveal phase information for complex mass terms.

The approach clarifies the role of source terms in phase detection.

Abstract

If the zeta function regularization is used and a complex mass term considered for fermions, the phase does not appear in the fermion determinant. This is not a drawback of the regularization, which can recognize the phase through source terms, as demonstrated by the anomaly equation which is explicitly derived here for a complex mass term.