Two body relativistic wave equations

TL;DR

This paper develops covariant relativistic wave equations for two interacting particles, explores their solutions, and applies numerical analysis to Coulomb interactions, providing a unified framework for scalar and fermion systems.

Contribution

It introduces a covariant formulation and quantization of two-particle systems for various particle types, including explicit equations and numerical analysis.

Findings

Derived relativistic wave equations for scalar and fermion pairs.

Analyzed spectrum and spherical wave solutions for free particles.

Numerically studied Coulomb interactions in two-particle systems.

Abstract

The relativistic quantum mechanics of two interacting particles is considered. We first present a covariant formulation of kinematics and of reduced phase space, giving a short outline of the classical results. We then quantize the systems for the scalar-scalar, fermion-scalar and fermion-fermion cases. We study the spectrum and the spherical waves solutions of the free case. The interaction with central scalar and vector potentials is introduced and the explicit equations are deduced. The one particle and the non relativistic limits are recovered and the general lines for the solution of the boundary value problems are given. We make a numerical analysis of the first two cases with Coulomb interaction. For the two fermions we largely revisit the model we had previously derived in order to uniformize the description for all the three cases. In order to give a complete review we report in Appendix some of the most interesting results obtained for atomic and mesonic systems with Coulomb and Cornell potential interactions respectively.