Axial anomaly in three dimensions and planar fermions

The origin and implications of the axial anomaly in three dimensions for fermions are discussed. Since the zero eigenvalue of the Dirac equation makes the partition function vanish, it is a singular point. The presence of the zero eigenvalue in the Dirac equation makes the functional space nontrivial topologically. An anomaly term is induced and a consistency condition emerges. The Hall conductivity is quantized and parity-violating light scattering occurs.