dorsal/arxiv
View SchemaThe doublet of Dirac fermions in the field of the non-Abelia monopole and parity selection rules
| Authors | V. M. Red'kov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9812067 |
| URL | https://arxiv.org/abs/quant-ph/9812067 |
Abstract
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, j^{2}, j_{3}, 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).
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"abstract": "The paper concerns a problem of Dirac fermion doublet in the external\nmonopole potential arisen out of embedding the Abelian monopole solution in the\nnon-Abe- lian scheme. In this particular case, the Hamiltonian is invariant\nunder some symmetry operations consisting of an Abelian subgroup in the complex\nrotational group SO(3.C). This symmetry results in a certain (A)-freedom in\nchoosing a discrete operator entering the complete set {H, j^{2}, j_{3}, N(A),\nK} . The same complex number A represents a parameter of the wave functions\nconstructed. The generalized inversion-like operator N(A) implies its own\n(A-dependent) de- finition for scalar and pseudoscalar, and further affords\nsome generalized N(A)-parity selection rules. It is shown that all different\nsets of basis func- tions Psi(A) determine the same Hilbert space. In\nparticular, the functions Psi(A) decompose into linear combinations of\nPsi(A=0). However, the bases con- sidered turn out to be nonorthogonal ones\nwhen A is not real number; the latter correlates with the non-self-conjugacy\nproperty of the operator N(A) at those A-s.\n (This is a shortened version of the paper).",
"arxiv_id": "quant-ph/9812067",
"authors": [
"V. M. Red\u0027kov"
],
"categories": [
"quant-ph"
],
"title": "The doublet of Dirac fermions in the field of the non-Abelia monopole and parity selection rules",
"url": "https://arxiv.org/abs/quant-ph/9812067"
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