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Paper   IPM / P / 6738
School of Physics
  Title:   Master Function Approach to Quantum Solvable Models on SL(2,c) and SL(2,c)/GL(1,c) Manifolds
1.  H. Fakhri
2.  M.A. Jafarizadeh
  Status:   Published
  Journal: J. Math. Phys.
  No.:  27
  Vol.:  41
  Year:  2000
  Pages:   505-546
  Supported by:  IPM
By introducing a new parameter as a second associated index for special functions, we construct the three-dimensional differential generators of gl(2,c) Lie algebra together with the corresponding contracted form h4. Non-Casimir quadratic as well as the Casimir of gl(2,c) (and h4) generators can be considered as quantum solvable models on group manifold SL(2,c). Then, by appropriate parametrization of group manifold SL(2,c) and eliminating one of the coordinates, we obtain quantum solvable Hamiltonians on homogeneous manifold SL(2,cGL(1,c) with the metric described by master function. We show that two-dimensional Hamiltonian on SL(2,cGL(1,c) derived from the reduction of Casimir operator so(4,c) Lie algebra as a three-dimensional Hamiltonian on group manifold SL(2,c), possesses the degeneracy SL(2,c) group and, also, the shape invariance property, where both have para-supersymmetry representations of arbitrary order.

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