1998/12/23 by V. M. Red'kov, Red'kov, V. M.
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9812067
15 pages, latex209
arxiv created 1998/12/23 · arxiv updated 2009/12/01
The paper concerns a problem of Dirac fermion doublet in the external monopole potential arisen out of embedding the Abelian monopole solution in the non-Abe- lian scheme. In this particular case, the Hamiltonian is invariant under some symmetry operations consisting of an Abelian subgroup in the complex rotational group SO(3.C). This symmetry results in a certain (A)-freedom in choosing a discrete operator entering the complete set H, j2, j3, N(A), K . The same complex number A represents a parameter of the wave functions constructed. The generalized inversion-like operator N(A) implies its own (A-dependent) de- finition for scalar and pseudoscalar, and further affords some generalized N(A)-parity selection rules. It is shown that all different sets of basis func- tions Psi(A) determine the same Hilbert space. In particular, the functions Psi(A) decompose into linear combinations of Psi(A=0). However, the bases con- sidered turn out to be nonorthogonal ones when A is not real number; the latter correlates with the non-self-conjugacy property of the operator N(A) at those A-s. (This is a shortened version of the paper).