Abstract
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 μ 2 = m 2 is the crucial point for Chern-Simons at zero temperature. So when μ 2 < m 2 the μ influence is absent and we obtain the usual Chern-Simons term. On the other hand, when μ 2 m 2 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.
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