  In the semiclassical approximation in which the electric charges of scalar
particles are described by Grassmann variables ($Q_i^2=0, Q_iQ_j\ne 0$), it is
possible to re-express the Lienard-Wiechert potentials and electric fields in
the radiation gauge as phase space functions, because the difference among
retarded, advanced, and symmetric Green functions is of order Q_i^2. By working
in the rest-frame instant form of dynamics, the elimination of the
electromagnetic degrees of freedom by means of suitable second classs
contraints leads to the identification of the Lienard-Wiechert reduced phase
space containing only N charged particles with mutual action-at-a-distance
vector and scalar potentials. A Darboux canonical basis of the reduced phase
space is found. This allows one to re-express the potentials for arbitrary N as
a unique effective scalar potential containing the Coulomb potential and the
complete Darwin one, whose 1/c^2 component agrees for with the known
expression. The effective potential gives the classical analogue of all static
and non-static effects of the one-photon exchange Feynman diagram of scalar
electrodynamics.
