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

Abstract

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 [Formula: see text]. Here, [Formula: see text] is the Lorentz boost generator in the unfaithful internal realization of the Poincaré group and its vanishing is the gauge-fixing to the rest-frame conditions [Formula: see text]. 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 electro-magnetic 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.