Towards relativistic atomic physics. Part 1. The rest-frame instant form of dynamics and a canonical transformation for a system of charged particles plus the electro-magnetic field

摘要

Abstract: A complete exposition of the rest-frame instant form of dynamics for arbitrary isolated systems (particles,nfields, strings, fluids) admitting a Lagrangian description is given. The starting point is the parametrized Minkowskintheory describing the system in arbitrary admissible noninertial frames in Minkowski space-time, which allows onento define the energy–momentum tensor of the system and to show the independence of the description from the clocknsynchronization convention and from the choice of the 3-coordinates. The restriction to the inertial rest frame, centered onnthe inertial observer having the Fokker–Pryce center-of-inertia world-line, and the study of relativistic collective variablesnreplacing the nonrelativistic center of mass lead to the description of the isolated system as a decoupled globally definednnoncovariant canonical external center of mass carrying a pole–dipole structure (the invariant mass M and the rest spinn¯ S of the system) and an external realization of the Poincaré group. Mc and ¯ S are the energy and angular momentum ofna unfaithful internal realization of the Poincaré group built with the energy–momentum tensor of the system and actingninside the instantaneous Wigner 3-spaces where all the 3-vectors are Wigner covariant. The vanishing of the internaln3-momentum and of the internal Lorentz boosts eliminate the internal 3-center of mass inside the Wigner 3-spaces, so thatnat the end the isolated system is described only by Wigner-covariant canonical internal relative variables. Then an isolatednsystem of positive-energy charged scalar articles with mutual Coulomb interaction plus a transverse electromagnetic fieldnin the radiation gauge is investigated as a classical background for defining relativistic atomic physics. The electric chargesnof the particles are Grassmann-valued to regularize the self-energies. The external and internal realizations of the Poincarénalgebra in the rest-frame instant form of dynamics are found. This allows one to define explicitly the rest-frame conditionsnand their gauge-fixings (needed for the elimination of the internal 3-center of mass) for this isolated system. It is shownnthat there is a canonical transformation that allows one to describe the isolated system as a set of Coulomb-dressedncharged particles interacting through a Coulomb plus Darwin potential plus a free transverse radiation field: these twonsubsystems are not mutually interacting (the internal Poincaré generators are a direct sum of the two components) and areninterconnected only by the rest-frame conditions and the elimination of the internal 3-center of mass. Therefore, in thisnframework with a fixed number of particles there is a way out from the Haag theorem, at least at the classical level.