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Paper   IPM / Physic / 6895
School of Physics
  Title:   Dirac Equation for A Spin-1/2 Charged Particle on the 2D Sphere S2 and the Hyperbolic Plane H2
  Author(s):  H. Fakhri
  Status:   Published
  Journal: J. Phys. A: Math. Gen.
  No.:  30
  Vol.:  35
  Year:  2002
  Pages:   6329-6337
  Supported by:  IPM
Using the idea of shape invariance with respect to the main quantum number n, we represent Lie algebras u(2) and u(1,1). The induced metric by the Casimir operator of Lie algebras u(2) and u(1,1) leads us to obtain new solutions of the Dirac equation corresponding to a spin−[1/2] charged particle on the 2D sphere S2 and the hyperbolic plane H2 in the presence of a magnetic monopole. It is shown that the related new spinors represent the supersymmetry algebra, and that they satisfy shape invariance equations with respect to n.

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