Master function approach to quantum solvable models on SL(2,c) and SL(2,c)/GL(1,c) manifolds

摘要

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 h(4). Non-Casimir quadratic as well as the Casimir of gl(2,c) (and h(4)) 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,c)/GL(1,c) with the metric described by master function. We show that two-dimensional Hamiltonian on SL(2,c)/GL(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. (C) 2000 American Institute of Physics. [S0022-2488(99)01212-8]. [References: 12]