CHERN-SIMONS TERM AT FINITE-DENSITY

The Chem-Simons topological term coefficient is derived at arbitrary f inite density. As it happens mu(2) = m(2) is the crucial point for Che m-Simons. So when mu(2) < m(2) the mu-influence disappears and we get the usual Chem-Simons term. On the other hand when mu(2) > m(2) the Ch em-Simons term vanishes because of the non zero density of background fermions. In particular for the massless case the parity anomaly is ab sent at any finite density. This result holds in any odd dimension bot h in the abelian and in the nonabelian case. (C) 1997 Published by Els evier Science B.V.