Gauge invariance, charge conservation, and axial anomaly in fermion-monopole interactions

Abstract

A gauge-invariant quantum field theory is formulated for a fermion-monopole system with the finite monopole size taken into account. It is shown that gauge invariance near and inside the monopole requires the inclusion of quantum fluctuations associated with the heavy charged bosons. Scattering of massless fermions is then considered, and an elementary exposition of the Rubakov-Callan effect is given by solving simultaneously the Dirac equation, Maxwell equations, and the axial-anomaly equation. Charge-conserving solutions are explicitly given which may or may not observe chirality. The solutions which break chirality require emission of charged fermions via the axial anomaly.