Commutation Rules and Eigenvalues of Spin and Orbital Angular Momentum of Radiation Fields

Abstract

We investigate the separation of the total angular momentum J of the electromagnetic field into a ‘spin’ part S and an ‘orbital’ part L. We show that both ‘spin’ and ‘orbital’ angular momentum are observables. However, the transversality of the radiation field affects the commutation relations for the associated quantum operators. This implies that neither S nor L are angular momentum operators. Moreover their eigenvalues are not discrete. We construct field modes such that each mode excitation (photon) is in a simultaneous eigenstate of S _z and L _z. We consider the interaction of such a photon with an atom and the resulting effect on the internal and external part of the atomic angular momentum.