The rest-frame Darwin potential from the Lienard-Wiechert solution in the radiation gauge (Q5950545)

The authors analyze how to extract the action-at-a-distance inter-particle potential hidden in the semi-classical Lienard-Wiechert solution of the electromagnetic field equations. The problem is formulated in the Wigner-covariant rest-frame instant form of dynamics, which (i) is defined on Wigner hyperplanes orthogonal to the total time-like four-momentum of the isolated system and (ii) requires the choice of the sign of the energy of the particles.