One-loop induced topological term in QED3

We consider the 2+1 dimensional massive QED and discuss the induced topological term in the one-loop level by using the higher derivative regularization. We show that the higher derivative regularization, which manifestly preserves the parity invariance when the fermion mass vanishes, automatically leads to a nonvanishing topological term in low energies. Although this higher derivative regularization formally violates the local gauge invariance, we propose a systematic way to recover the gauge invariance by adding local counter terms dictated by Ward-Takahashi identities. In practical applications, this regularization is interesting in connection with the discussion of the dynamical origin of the quantum Hall effect.