On the angular momentum of photons: effects of transversality condition on the quantization of radiation fields

Abstract

The notion of intrinsic system of coordinates is introduced for the photon from the constraint of transversality condition. The degree of freedom to specify the intrinsic system is extracted from the same constraint, which turns out to be responsible for the spin Hall effect of light. It is shown that the fundamental quantization conditions that break down in the laboratory system of coordinates restore in the intrinsic system, which make it realizable to canonically quantize the radiation field. It is also shown that the dependence of the intrinsic system on the momentum underlies the noncommutativity of photon position in the laboratory system. The commutation relations of the spin and orbital angular momentum that were found by van Enk and Nienhuis [J. Mod. Opt. \textbf{41}, 963 (1994)] in a second quantized theory are re-derived in the present first quantized theory.