Relativistic Corrections in a Three-Boson System of Equal Masses

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.

16 pages, no figure. Several points clarified, one typo corrected. References added. To appear in Physical Review A

References in corpus (4)

• The relativistic two-body potentials of constraint theory from summation of Feynman diagrams
• 3D reduction of the N-body Bethe-Salpeter equation
• Reduction of relativistic three-body kinematics
• Binding Energy in Two and Three-Body Relativistic Dynamics

Cited by in corpus (1)

• Relativistic oscillator model with spin for nucleon resonances