On the Definition of Spin for a Radiation Field [1942e]

Abstract

Using the general expression (1) for the energy-momentum tensor of any field, it is possible to define the spin or intrinsic angular momentum of the field, contained in a given region. But it is clear that this definition is ambiguous due to the fact that a certain integral over the surface of the domain under consideration can be retained or omitted at will in this definition; and, for a radiation field, this integral might very well be different from zero. Let us define a radiation field to be a field the amplitude of which at a distance R from a fixed point does not fall off more rapidly than R ⁻¹. The purpose of this note is simply to show that in this case the flux of spin carried by the radiation field — which is in fact the quantity having a direct physical significance — is not affected by the ambiguity in question. For a better understanding, we will summarize, as briefly as possible, the entire problem.