Parity anomaly in Dirac equation in (1+2) dimensions, quantum electrodynamics and pair production

We show that parity operator plays an interesting role in Dirac equation in (1+2) dimensions and can be used for defining chiral charges. Further the "anomalous" current induced by an external gauge field can be related to the anomalous divergence of an axial vector current which arises due to quantum radiative corrections provided by triangular loop Feynman diagrams in analogy with the corresponding axial anomaly in (1+3) dimensions. It is shown that the nonconservation of "chiral charge" due to anomaly is related with the topological Chern–Simons charge. As an application pair creation of massless fermions in electric field is discussed.