Multiplicative anomaly and finite charge density

TL;DR

This paper investigates the multiplicative anomaly in zeta-function regularized determinants and its physical implications for charged bosonic fields at finite charge density, highlighting an overlooked term that can affect calculations.

Contribution

It introduces and discusses the physical relevance of the multiplicative anomaly term in zeta-function regularization, especially for finite charge density systems.

Findings

The multiplicative anomaly can produce additional terms in functional determinants.

This anomaly has significant implications for charged bosonic fields at finite charge density.

Potential applications extend to other areas involving matrix differential operators.

Abstract

When dealing with zeta-function regularized functional determinants of matrix valued differential operators, an additional term, overlooked until now and due to the multiplicative anomaly, may arise. The presence and physical relevance of this term is discussed in the case of a charged bosonic field at finite charge density and other possible applications are mentioned.