Role of Spin in the Monopole Problem

Abstract

The scattering of an electric charge from a magnetic monopole is discussed in a way which explicitly incorporates conservation of angular momentum. The Dirac quantization condition for the physical charges is derived from the correspondence principle and the requirement of rotational invariance. The same discussion shows that the initial and final states of the scattering reaction contain an extra spin, which cannot be associated with either particle alone. In the classical nonrelativistic theory it is known that such an extra spin appears, and that it may be identified with the angular momentum of the electromagnetic field. A quantized version of this nonrelativistic spin theory is obtained and shown to be equivalent to the Dirac theory based on a singular vector potential. The spin approach gives an interesting perspective on the relativistic monopole problem. Among the standard $S$-matrix postulates, that of crossing symmetry must be modified or abandoned if a relativistic theory is to succeed.