Eikonal model with covariant recoil in relativistic quantum field theory in terms of a correlation expansion

A technique to derive covariant recoil to the eikonal model in relativistic quantum field theory is developed. Recoil is defined relative to the rectilinear-path approximation which gives the eikonal model. It appears in terms of a partially factorizable correlation expansion, where the first term is noncorrelated and is the usual eikonal model. The second term displays pair correlations, etc. By correlation here we mean dynamical correlation. Kinematical correlations due to four-momentum conservation are of course superimposed everywhere. We first consider soft recoil, and then generalize to the hard recoil, without introducing any cutoff. The technique is developed here for a scalar φ³-type theory but it is general enough to be extended to, for example, quantum electrodynamics and scalar electrodynamics.