Relativistic oscillator model with spin for nucleon resonances

Abstract

AbstractThe relativistic three-body problem is approached via the extension of the SL(2, C) group to the Sp(4, C) one. In terms of Sp(4, C) spinors, a Dirac-like equation with three-body kinematics is composed. After introducing the linear in coordinates interaction, it describes the spin-1/2 oscillator. For this system, the exact energy spectrum is derived and then applied to fit the Regge trajectories of baryon N-resonances in the (E 2, J) plane. The model predicts linear trajectories at high total energy E with some form of nonlinearity at low E.