Towards relativistic atomic physics. Part 2. Collective and relative relativistic variables for a system of charged particles plus the electromagnetic field

摘要

In this second paper we complete the classical description of an isolated system of "charged positive-energy particles, with Grassmann-valued electric charges and mutual Coulomb interaction, plus a transverse electromagnetic field" in the rest-frame instant form of dynamics. In particular, we show how to determine a collective variable associated with the internal 3-center of mass on the instantaneous 3-spaces, to be eliminated with the constraints K-(int) approximate to 0. Here, K-(int) is the Lorentz boost generator in the unfaithful internal realization of the Poincare group and its vanishing is the gauge fixing to the rest-frame conditions P-(int) approximate to 0. We show how to find this collective variable for the following isolated systems: (a) charged particles with a Coulomb plus Darwin mutual interaction; (b) transverse radiation field; (c) charged particles with a mutual Coulomb interaction plus a transverse electromagnetic field. Then we define the Dixon multipolar expansion for the open particle subsystem. We also define the relativistic electric-dipole approximation of atomic physics in the rest-frame instant form and we find a possible relativistic generalization of the electric-dipole representation.