AXIAL ANOMALY IN THE PRESENCE OF THE AHARONOV-BOHM GAUGE FIELD

We investigate on the plane the axial anomaly for Euclidean Dirac ferm ions in the presence of a background Aharonov-Bohm gauge potential. Th e nonperturbative analysis depends on the selfadjoint extensions of th e Dirac operator and the result is shown to be influenced by the actua l way of understanding the local axial vector current. The role of the quantum mechanical parameters involved in the expression for the axia l anomaly is discussed. A derivation of the effective action by means of the stereographic projection is also considered.