Towards Relativistic Atomic Physics. I. The Rest-Frame Instant Form of Dynamics and a Canonical Transformation for a System of Charged Particles plus the Electro-Magnetic Field

TL;DR

This paper develops a relativistic framework for atomic physics using the rest-frame instant form of dynamics, canonical transformations, and a regularized charged particle model, enabling a clear separation of particle and field subsystems.

Contribution

It introduces a canonical transformation for charged particles plus electromagnetic field in a relativistic setting, facilitating the analysis of atomic systems at the classical level.

Findings

Canonical transformation separates particles and field subsystems

System described by Coulomb-dressed particles and free radiation field

Framework avoids Haag theorem issues at classical level

Abstract

A complete exposition of the rest-frame instant form of dynamics for arbitrary isolated systems (particles, fields, strings, fluids)admitting a Lagrangian description is given. The starting point is the parametrized Minkowski theory describing the system in arbitrary admissible non-inertial frames in Minkowski space-time, which allows one to define the energy-momentum tensor of the system and to show the independence of the description from the clock synchronization convention and from the choice of the 3-coordinates. In the inertial rest frame the isolated system is seen as a decoupled non-covariant canonical external center of mass carrying a pole-dipole structure (the invariant mass $M$ and the rest spin ${\vec {\bar S}}$ of the system) and an external realization of the Poincare' group. Then an isolated system of positive-energy charged scalar articles plus an arbitrary electro-magnetic field in the radiation gauge is investigated as a classical background for defining relativistic atomic physics. The electric charges of the particles are Grassmann-valued to regularize the self-energies. The rest-frame conditions and their gauge-fixings (needed for the elimination of the internal 3-center of mass) are explicitly given. It is shown that there is a canonical transformation which allows one to describe the isolated system as a set of Coulomb-dressed charged particles interacting through a Coulomb plus Darwin potential plus a free transverse radiation field: these two subsystems are not mutually interacting and are interconnected only by the rest-frame conditions and the elimination of the internal 3-center of mass. Therefore in this framework with a fixed number of particles there is a way out from the Haag theorem,at least at the classical level.