Electromagnetic angular momentum and quantum mechanics

Abstract

A quick way of arriving at the Dirac quantization condition between electric and magnetic charges is to require that the electromagnetic field angular momentum of a Thomson dipole (a magnetic monopole and an electric charge) equal some integer multiple of the fundamental unit of quantum mechanical angular momentum, ℏ/2. Applying this same type of argument to the electromagnetic field angular momentum carried by a magnetic dipole–electric charge system leads to an infinite number of different quantization conditions, and an apparent incompatibility between quantum mechanics and the dipole–charge system. However, a more careful analysis shows that the particle plus field angular momentum of this system does satisfy the standard angular momentum commutation relationships and is therefore a good quantum mechanical angular momentum. This emphasizes that caution must be taken when applying such semiclassical quantization arguments. Finally, a possible connection between this dipole–charge field angular momentum and the nucleon spin crisis is given.