The induced Chern–Simons term at finite temperature

It is argued that the derivative expansion is a suitable method to deal with finite temperature field theory, if it is restricted to spatial derivatives only. Using this method, a simple and direct calculation is presented for the radiatively induced Chern–Simons-like piece of the effective action of (2+1)-dimensional fermions at finite temperature coupled to external gauge fields. The gauge fields are not assumed to be subjected to special constraints, and in particular, they are not required to be stationary nor Abelian.