Induced Parity-Breaking Term at Finite Chemical Potential and Temparature

We exactly calculated the parity-odd term of the effective action induced by the fermions in 2+1 dimensions at finite chemical potential and finite temperature. It shows that gauge invariance is still respected. A more gerneral class of background configurations is considered. The knowledge of the reduced 1+1 determinant is required in order to draw exact conclusions about the gauge invariance of the parity-odd term in this latter case.