Infinite Set of Quasipotential Equations from the Kadyshevsky Equation

Abstract

We show that by modifying the propagator in the Kadyshevsky equation, we can obtain an infinite set of quasipotential equations which satisfy both Lorentz covariance and elastic unitarity and of which the Logunov-Tavkhelidze-Blankenbecler-Sugar-Alessandrini-Omnes equation and the Gross equation are special cases. We also show that the perturbation scheme of Chen and Raman, for using the quasipotential equation to obtain approximations to the Bethe-Salpeter equation, can be greatly simplified by the use of resolvent-identity-type arguments.