Electric Charge in Composite Magnetic Monopole Theories

Abstract

It is observed that the spin approach to the interaction of electric charges with magnetic monopoles leads naturally to theories with composite monopoles made from SU(2) gauge fields. The key steps are to express the “electromagnetic field angular momentum” associated with a charge-pole system as a quantum-mechanical spin operator (as was done some years ago) and then to identify this spin operator as the generator of SU(2) transformations on charged-particle wave functions. It is emphasized that composite monopoles may not occur unless electric charge is one of the operators of an SU(2) symmetry. The formalism for conservation of electric charge, and quantization of the electric charge of a monopole, is developed at a “first-quantized” level. Speculations are given on high energy charge-pole scattering. Some problems with second quantization are discussed, and the possibility is raised that there may be an infinite mass renormalization of a composite monopole which has finite mass in the classical approximation.