Instantaneous Bethe-Salpeter Equation with Exact Propagators
  Consequent application of the instantaneous approximation to both the interaction and all propagators of the bound-state constituents allows us to forge, within the framework of the Bethe-Salpeter formalism for the description of bound states, an instantaneous form of the Bethe-Salpeter equation with exact (i.e., full) propagators of the bound-state constituents. This instantaneous equation generalizes the well-known Salpeter equation the derivation of which needs the additional assumption of free propagation of the bound-state constituents. 
Wolfgang Lucha and F.F. Schoberl