CLASSICAL ANOMALIES FOR SPINNING PARTICLES

We discuss the phenomenon of classical anomaly. It is observed for 3D Berezin-Marinov (BM), Barducci-Casalbuoni-Lusanna (BCL) and Cortes-Ply ushchay-Velazquez (CPV) pseudoclassical spin particle models. We show that quantum mechanically these different models correspond to the sam e P,T-invariant system of planar fermions, but the quantum system has global symmetries being not reproducible classically in full in any of the models. We demonstrate that the specific U(1) gauge symmetry char acterized by the opposite coupling constants of spin s = +1/2 and s = -1/2 states has a natural classical analog in the CPV model but can be reproduced in the BM and BCL models in an obscure and rather artifici al form. We also show that the BM and BCL models quantum mechanically are equivalent in any odd-dimensional space-time, but describe differe nt quantum systems in even space-time dimensions. (C) 1998 Elsevier Sc ience B.V.