Relation between Bethe-Salpeter and Schroedinger wave functions for many-particle systems

The connection is made between a many-time approach to S-matrix elements and energy eigenvalues, which naturally arises from a field theoretical point of view, and the single time Schroedinger- and Breit-like formalism often used in detailed calculations for many-particle systems, such as many-electron atoms. Specifically, the many-particle Bethe-Salpeter equation is expressed in terms of the corresponding Schroedinger equation for the non-relativistic case in which the Bethe-Salpeter kernel consists of only two-particle local static interactions. Also, the one-photon transition matrix element for this case in the Bethe-Salpeter formalism is shown to be equivalent to the corresponding well-known Schroedinger result. The treatment developed is well suited to systematic relativistic generalization. (orig.)