CHIRAL AND PARITY ANOMALIES AT FINITE TEMPERATURE AND DENSITY

Two closely related topological phenomena are studied at finite density and temperature. These are the chiral anomaly and the Chern-Simons term. Using different methods it is shown that μ2 = m2 is the crucial point for Chern-Simons at zero temperature. So when μ2 < m2 the μ influence is absent and we obtain the usual Chern-Simons term. On the other hand, when μ2m2 the Chern-Simons term vanishes because of the non-zero density of the background fermions. The chiral anomaly does not depend on density and temperature. The connection between 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.