Angular momentum and space–time hyperboloids

Abstract

For a classical field theory, in Minkowski space–time, the field momentum and angular momentum are defined as an integral of the appropriate density over an asymptotically null hyperboloid. We prove that for the electromagnetic field these quantities are well defined even for charged sources where infrared divergences are a problem for defining the angular momentum. Moreover, it is also shown that if the angular momentum density is integrated over a null plane, the angular momentum is not well defined for charged sources.