CHIRAL AND PARITY ANOMALIES AT FINITE-TEMPERATURE AND DENSITY

Two closely related topological phenomena are studied at finite densit y and temperature. These are the chiral anomaly and the Chern-Simons t erm. Using different methods it is shown that mu(2) = m(2) is the cruc ial point for Chern-Simons at zero temperature. So when mu(2) < m(2) t he mu influence is absent and we obtain the usual Chern-Simons term. O n the other hand, when mu(2) > m(2) the Chern-Simons term vanishes bec ause of the non-zero density of the background fermions, The chiral an omaly does not depend on density and temperature. The connection betwe en parity anomalous Chern-Simons and the chiral anomaly is generalized at finite density, These results hold in any dimension in abelian and in non-abelian cases. (C) 1998 Published by Elsevier Science B.V.