Chiral And Parity Anomalies At Finite Temperature And Density

Abstract

Two closely related topological phenomena are studied at finite density and temperature. These are chiral anomaly and Chern-Simons term. By using different methods it is shown that ${\mu }^2=m^2$ is the crucial point for Chern-Simons at zero temperature. So when ${\mu }^2<m^2$ $\mu$--influence disappears and we get the usual Chern-Simons term. On the other hand when ${\mu }^2>m^2$ the Chern-Simons term vanishes because of non-zero density of background fermions. It is occurs that the chiral anomaly doesn't depend on density and temperature. The connection between parity anomalous Chern-Simons and chiral anomaly is generalized on finite density. These results hold in any dimension as in abelian, so as in nonabelian cases.

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