U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator

Joseph N. Ginocchio
Phys. Rev. Lett. 95, 252501 – Published 13 December 2005

Abstract

We show that a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials has not only a spin symmetry but a U(3) symmetry and that a Dirac Hamiltonian with scalar and vector harmonic oscillator potentials equal in magnitude but opposite in sign has not only a pseudospin symmetry but a pseudo-U(3) symmetry. We derive the generators of the symmetry for each case.

  • Received 12 August 2005

DOI:https://doi.org/10.1103/PhysRevLett.95.252501

©2005 American Physical Society

Authors & Affiliations

Joseph N. Ginocchio

  • MS B283, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

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Issue

Vol. 95, Iss. 25 — 16 December 2005

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