  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.
