Reduction of relativistic three-body kinematics

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.

Comments: LaTeX file, 28 pages. Presentation improved; many points clarified. Several misprints and the expression for $\Gamma (0)$ are corrected. Display of approximate cluster separability. Velocity of light is restored in the formulas, the nonrelativistic limit is considered