Relativistic Quantum Mechanics of Two Interacting Particles

A variation of the quasipotential approach of Logunov and Tavkhelidze is investigated. Two relativistic particles with or without spin are subjected to a mutual interaction that can be described (i) as generated by the exchange of field quanta or (ii) as a two-particle potential $V\left(\mathrm{r}\right)$ that depends on the relativistic three-dimensional coordinates introduced by Kadyshevsky. The framework includes the complete axiomatic structure of nonrelativistic quantum mechanics (except that the metric in Hilbert space is indefinite in the same way as in the static Klein-Gordon or Dirac theories) and is at the same time fully and explicitly covariant. Both the nonrelativistic and the classical limits exist and are susceptible to detailed interpretation. The case of two spinless particles with a "relativistic Coulomb" interaction is examined in detail. The wave equation, as well as the equation for the $T$ matrix, is in this case exactly soluble. Closed analytic expressions are given for transition form factors, including "photoproduction," the elastic scattering amplitude, and a production amplitude (bremsstrahlung).