Relativistic two-body equation based on the extension of the SL(2,C) group

Abstract

A new approach to the two-body problem based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one is developed. The wave equation with various forms of including the interaction for the system of the spin-1/2 and spin-0 particles is constructed. For this system, it was found that the wave equation with a linear confinement potential involved in the non-minimal manner has an oscillator-like form and possesses the exact solution.

arXiv comment9 pages, no figures

References in corpus (5)

• Tests of Two-Body Dirac Equation Wave Functions in the Decays of Quarkonium and Positronium into Two Photons
• The relativistic two-body potentials of constraint theory from summation of Feynman diagrams
• QCD string and the Lorentz nature of confinement
• On unique parametrization of the linear group GL(4.C) and its subgroups by using the Dirac matrix algebra basis
• Direct experimental test of scalar confinement

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• A new two-body relativistic potential model for pionic hydrogen
• Relativistic oscillator model with spin for nucleon resonances