The rest-frame Darwin potential from the Lienard-Wiechert solution in the radiation gauge

In the semiclassical approximation in which the electric charges of scalar particles are described by Grassmann variables (Q(i)(2) = 0, Q(i)Q(j) not e qual 0), it is possible to re-express the Lienard-Wiechert potentials and e lectric fields in the radiation gauge as phase space functions, because the difference among retarded, advanced, and symmetric Green functions is of o rder Q(i)(2). By working in the rest-frame instant form of dynamics, the el imination of the electromagnetic degrees of freedom by means of suitable se cond class contraints leads to the identification of the Lienard-Wiechert r educed phase space containing only N charged particles with mutual action-a t-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 Coul omb potential and the complete Darwin one, whose 1/c(2) component agrees wi th the known expression. The effective potential gives the classical analog ue of all static and non-static effects of the one-photon exchange Feynman diagram of scalar electrodynamics. 2001 Academic Press.