Regularization schemes and the multiplicative anomaly

TL;DR

The paper demonstrates that the multiplicative anomaly observed in zeta-function regularization of scalar fields is not a physical effect but a regularization artifact, which can be avoided or removed with alternative schemes or renormalization choices.

Contribution

It shows that the multiplicative anomaly is scheme-dependent and can be eliminated, clarifying that it does not represent new physical phenomena.

Findings

No anomaly with alternative regularization schemes

Anomalies can be removed by choosing different renormalization scales

Multiplicative anomalies are artifacts of specific regularization methods

Abstract

Elizalde, Vanzo, and Zerbini have shown that the effective action of two free Euclidean scalar fields in flat space contains a `multiplicative anomaly' when zeta-function regularization is used. This is related to the Wodzicki residue. I show that there is no anomaly when using a wide range of other regularization schemes and further that this anomaly can be removed by an unusual choice of renormalisation scales. I define new types of anomalies and show that they have similar properties. Thus multiplicative anomalies encode no novel physics. They merely illustrate some dangerous aspects of zeta-function and Schwinger proper time regularization schemes.