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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.

http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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