Reduction of Relativistic Three-Body Kinematics

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. Introducing mutual interactions provides a model which is (at least for three equal masses) tractable and admits a reasonable nonrelativistic limit.