Long-range effects in asymptotic fields and angular momentum of classical field electrodynamics

Asymptotic properties of classical field electrodynamics are considered. Special attention is paid to the long-range structure of the electromagnetic field. It is shown that conserved Poincar6 quantities may be expressed in terms of the asymptotic fields. Long-range variables are shown to be responsible for an angular momentum contribution which mixes Coulomb and infrared free field characteristics; otherwise angular momentum and energy-momentum separate into electromagnetic and mat- ter fields contributions. C 1995 American Institute of Physics. In the present work we try to better understand the long-range structure of electrodynamics in classical field theory. We believe that in this way one can gain new insights into the quantum case as well. The domain in which the classical structure is most likely to be of some relevance for the quantum case is the asymptotic region. Rigorous results on the asymptotics of electromagnetic field are presented in Sec. II and on the asymptotics of Dirac field in Sec. IV. The results are relevant for the interacting theory, as argued in Secs. II and V. In that case, some additional assumptions are made which seem plausible, but remain unproved. Our main objective, when discussing the asymptotic fields, is the description of the specific way how matter and radiation separate in the asymptotic regions. In this respect, the approach of the present paper differs from that of Flato, Simon, and Taflin, who have recently described rigorous results on Cauchy problem and scattering states in classical Maxwell-Dirac theory; 7 see also a comment in Sec. V. Using results on asymptotic fields we express energy momentum and angular momentum of the system in terms of those fields. We stress that our aim is not a purely mathematical study in classical field theory. Rather, with quantization in mind, we try to get a reasonably well-founded notion of the asymptotic structure of fields and conserved Poincar6 quantities.