Relativistic Corrections in a Three-Boson System of Equal Masses

TL;DR

This paper develops a relativistic framework for three-boson systems, simplifies the equations for equal masses, and computes first-order relativistic corrections beyond the nonrelativistic approximation, using a harmonic interaction as a model.

Contribution

It introduces a method to reduce relativistic three-boson equations to a manageable form and calculates first-order corrections for equal-mass systems.

Findings

Reduced the three-body relativistic problem to a three-dimensional eigenvalue problem.

Derived first-order relativistic corrections beyond the nonrelativistic limit.

Demonstrated the approach with a harmonic interaction model.

Abstract

Three-body systems of scalar bosons are described in the framework of relativistic constraint dynamics. With help of a change of variables followed by a change of wave function, two redundant degrees of freedom get eliminated and the mass-shell constraints can be reduced to a three-dimensional eigenvalue problem. In general, this problem is complicated, but for three equal masses a drastic simplification arises at the first post-Galilean order: the reduced wave equation becomes tractable, and we can compute a first-order correction beyond the nonrelativistic limit. The harmonic interaction is displayed as a toy model.