U(3) and pseudo-U(3) symmetry of the relativistic harmonic oscillator.
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.
Ginocchio
Joseph N
JN
MS B283, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.