Relativistic wave equations for the dynamics of two interacting particles

Abstract

We construct relativistic wave equations describing the dynamics of two interacting particle systems involving spin-0 bosons and/or spin-(1/2) fermions. The method consists in quantizing the manifestly covariant formalism with constraints of classical relativistic Hamiltonian mechanics. In this formalism the two-particle wave function satisfies two independent wave equations, which thus determine in a definite way its relative time evolution. We solve the compatibility condition of the two wave equations and classify the general classes of interaction potentials according to their tensor structure. We outline the relationship of this framework of relativistic quantum mechanics with the Bethe-Salpeter equation and its sector of normal solutions.