Chiral and parity anomalies at finite temperature and density Original Research Article

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.