A Particle‐Picture Approach to Anomalies in Chiral Gauge Theories

The system of a chiral fermion field coupled to a background gauge field is considered. By taking what we call the particle picture and carefully defining the S ‐matrix in the Heisenberg picture, we investigate anomalous phenomena in this system. It is shown by explicit calculations that the gauge‐field configuration with nonvanishing topological‐charge causes anomalous production of particles that is directly responsible for the chiral U (1) anomaly. Unlike the chiral U (1) anomaly, the gauge anomaly, that is, gauge non‐invariance of the S ‐matrix is a problem that arises in the phase of the S ‐matrix. It is shown that this phase is related to the freedom existing in the quantization method, and that a suitably chosen phase which of course is consistent with the equation of motion can remove the gauge anomaly. Finally, a modified form of path‐integral quantization for this system is proposed.