Role of retardation in 3-D relativistic equations

Abstract

Equal-time Green's function is used to derive a three-dimensional integral equation from the Bethe-Salpeter equation. The resultant equation, in the absence of anti-particles, is identical to the use of time-ordered diagrams, and has been used within the framework of ${\varphi }^2\sigma$ coupling to study the role of energy dependence and non-locality when the two-body potential is the sum of $\sigma$-exchange and crossed $\sigma$ exchange. The results show that non-locality and energy dependence make a substantial contribution to both the on-shell and off-shell amplitudes.

Comments: 17 pages, RevTeX; 8 figures. Accepted for publication in Phys. Rev. C56 (Nov. 97)