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

Joseph N. Ginocchio
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Abstract

We show that a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials has not only a spin symmetry but an 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.

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Joseph N. Ginocchio. 2005-12-13. U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator. https://doi.org/10.1103/physrevlett.95.252501

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