Regularization schemes and the multiplicative anomaly

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.Comment: 11 pages, LaTeX2e, major revision 15th December 1998 with focus now on renormalisation scales. Appendix and a few minor comments included which are not in Phys.Lett.B. published versio