Path integral formalism for finite-temperature field theory and generation of chiral currents

With the use of the path integral formalism for finite-temperature field theory, I find the persisting vector and axial currents that are generated in quantum chiral fermionic systems. The role of the explicit violation of chiral symmetry by fermion mass is elucidated. For the case of quantum fermionic systems in the backround of an arbitrary smooth magnetic field, I show that the chiral magnetic effect is substantiated on equally the same footing as the chiral separation effect is. Both effects remain unaltered if chiral symmetry is violated by mass.