Regularization schemes and the multiplicative anomaly

Details Regularization schemes and the multiplicative anomaly Regularization schemes and the multiplicative anomaly

1998-03-23

arxiv.org/abs/hep-th/9803184v3

Phys.Lett. B457 (1999) 127-132

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX2e, major revision 15th December 1998 with focus now on renormalisation scales. Appendix and a few minor commen

Scientific paper

10.1016/S0370-2693(99)00503-1

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.

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