Reduction of relativistic three-body kinematics

TL;DR

This paper reformulates the Klein-Gordon three-body system into a covariant, reduced form by transforming momenta, eliminating redundancies, and enabling a more tractable model for studying relativistic three-body interactions.

Contribution

It introduces a new covariant formulation of the three-body Klein-Gordon system that simplifies the equations by reducing degrees of freedom and facilitates the inclusion of interactions.

Findings

Reduces the Klein-Gordon three-body equations to a covariant three-dimensional form.

Maintains equivalence with the original system in relevant energy regimes.

Provides a tractable model for relativistic three-body interactions.

Abstract

The Klein-Gordon system describing three scalar particles without interaction is cast into a new form, by transformation of the momenta. Two redundant degrees of freedom are eliminated; we are left with a covariant equation for a reduced wave function with three-dimensional arguments. This new formulation of the mass-shell constraints is equivalent to the original KG system in a sector characterized by positivity of the energies and, if the mass differences are not too large, by a moderately relativistic regime. Then, mutual interaction is introduced and produces a tractable model.