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

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

2005-12-13

arxiv.org/abs/nucl-th/0512050v1

Phys.Rev.Lett. 95 (2005) 252501

Physics

Nuclear Physics

Nuclear Theory

8 pages, 0 figures, pusblished in Physical Review Letters 95, 252501 (2005)

Scientific paper

10.1103/PhysRevLett.95.252501

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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