Generalized Spin and Pseudo-Spin Symmetry: Relativistic Extension of Supersymmetric Quantum Mechanics
arXiv:1010.1831 · doi:10.1016/j.physletb.2011.04.019
Abstract
We consider the Dirac equation in 1+1 space-time dimension with vector, scalar and pseudo-scalar coupling. In the traditional spin (or pseudo-spin) symmetry, the difference between (or sum of) the scalar and vector potentials is a constant. Here, however, we introduce an alternative symmetry where the scalar or pseudo-scalar potential is proportional to the vector potential. This leads to a model with significant extensions to supersymmetric quantum mechanics. We present a formal solution of the problem but give explicit analytic results for specific examples.
9 pages
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