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.

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

References in corpus (5)

• Relativistic calculation of the triton binding energy and its implications
• 3D reduction of the N-body Bethe-Salpeter equation
• A cluster-separable Born approximation for the 3D reduction of the three-fermion Bethe-Salpeter equation
• Two and three-fermion 3D equations deduced from Bethe-Salpeter equations
• Binding Energy in Two and Three-Body Relativistic Dynamics

Cited by in corpus (4)

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• Relativistic action-at-a-distance interactions: Lagrangian and Hamiltonian to terms of second order
• A relativistic action-at-a-distance description of gravitational interactions?
• Relativistic Corrections in a Three-Boson System of Equal Masses