Relativistic oscillator model with spin for nucleon resonances

Abstract

Abstract:The relativistic three-body problem is approached via the extension of the SL(2 C ) group to the S (4 C ) one. In terms of S (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. PACS

Topological, noninertial and spin effects on the 2D Dirac oscillator in the presence of the Aharonov–Casher effect

“…Since that the relativistic version of the quantum harmonic oscillator (QHO) for spin-1/2 particles was formulated in the literature in 1989 by M. Moshinsky and A. Szczepaniak, the so-called Dirac oscillator (DO) [1], several works on this model have been and continue being performed in different areas of physics, such as in thermodynamics [2,3], nuclear physics [4][5][6], quantum chromodynamics [7,8], quantum optics [9,10], and graphene physics [11][12][13]. Besides that, the OD also is studied in other interesting physical contexts, such as in quantum phase transitions [14,15], noncommutative spaces [16,17], minimal length scenario [18,19], supersymmetry [20,21], etc.…”