Canonical and quasicanonical realizations of the osp(D vertical bar d) superalgebra and the Coulomb problem in superspaces

Canonical and quasi-canonical realizations of the osp(D\d) superalgebra are presented. In these realizations there is only one independent Casimir ope rator: The quadratic one C, the eigenvalues of which allow specification of the involved representations. Pauli's method for solving the spectrum of t he Coulomb problem through quantization of the Runge-Lenz vector is extende d to an arbitrary dimension superspace E(D\d) with D bosonic coordinates an d d (even) fermionic coordinates. The symmetry algebra of the Hamiltonian i s the superalgebra osp(D + 1\d). It is shown how the energy spectrum is rel ated to the Casimir operator C' of osp(D + 1\d) in its quasicanonical reali zation. Then the energy levels are given in terms of the eigenvalues of the operator C'. (C) 1998 American Institute of Physics. [S0022-2488(98)02210- 5].