There is no new physics in the multiplicative anomaly

TL;DR

The paper clarifies that the multiplicative anomaly does not introduce new physics but ensures consistency among different expressions for the effective action in quantum field theory at finite temperature and density.

Contribution

It demonstrates that the multiplicative anomaly's role is to maintain equality among effective action expressions, not to imply new physical phenomena.

Findings

The multiplicative anomaly does not lead to new physics.

Physical considerations determine the correct effective action expression.

The study compares non-relativistic and relativistic cases.

Abstract

We discuss the role of the multiplicative anomaly for a complex scalar field at finite temperature and density. It is argued that physical considerations must be applied to determine which of the many possible expressions for the effective action obtained by the functional integral method is correct. This is done by first studying the non-relativistic field where the thermodynamic potential is well-known. The relativistic case is also considered. We emphasize that the role of the multiplicative anomaly is not to lead to new physics, but rather to preserve the equality among the various expressions for the effective action.