dorsal/arxiv
View SchemaOn intrinsic structure of wave function of fermion triplet in external monopole field
| Authors | V. M. Red'kov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9902034 |
| URL | https://arxiv.org/abs/quant-ph/9902034 |
Abstract
Using the Weyl-Tetrode-Fock spinor formalism, the fermion triplet in the 't Hooft-Polyakov monopole field is examined all over again. Spherical solutions corresponding to the total conserved momentum J =l + S + T are constructed. The angular dependence is expressed in terms of the Wigner's functions. The radial system of 12 equations decomposes into two sub-systems by diagonalizing some complicated inversion operator. The case of minimal j = 1/2 is considered separately. A more detailed analysis is accomplished for the case of simplest monopole field: namely, the one produced by putting the Dirac potential into the non-Abelian scheme. Now a discrete operation diagonalized contains an additional complex parameter A. The same parameter enters wave functions. This quantity can manifest itself at matrix elements. In particular, there have been analyzed the N(A)-parity selection rules: those depending on the A. As shown, the A-freedom is a consequence of the existence of additional symmetry of the relevant Hamiltonian. The wave functions exhibit else one kind of freedom: B-freedom associated in turn with its own symmetry of the Hamiltonian. There has been examined both A and B-transformations relating functions associated with different A and B.
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"abstract": "Using the Weyl-Tetrode-Fock spinor formalism, the fermion triplet in the \u0027t\nHooft-Polyakov monopole field is examined all over again. Spherical solutions\ncorresponding to the total conserved momentum J =l + S + T are constructed. The\nangular dependence is expressed in terms of the Wigner\u0027s functions. The radial\nsystem of 12 equations decomposes into two sub-systems by diagonalizing some\ncomplicated inversion operator. The case of minimal j = 1/2 is considered\nseparately. A more detailed analysis is accomplished for the case of simplest\nmonopole field: namely, the one produced by putting the Dirac potential into\nthe non-Abelian scheme. Now a discrete operation diagonalized contains an\nadditional complex parameter A. The same parameter enters wave functions. This\nquantity can manifest itself at matrix elements. In particular, there have been\nanalyzed the N(A)-parity selection rules: those depending on the A. As shown,\nthe A-freedom is a consequence of the existence of additional symmetry of the\nrelevant Hamiltonian. The wave functions exhibit else one kind of freedom:\nB-freedom associated in turn with its own symmetry of the Hamiltonian. There\nhas been examined both A and B-transformations relating functions associated\nwith different A and B.",
"arxiv_id": "quant-ph/9902034",
"authors": [
"V. M. Red\u0027kov"
],
"categories": [
"quant-ph"
],
"title": "On intrinsic structure of wave function of fermion triplet in external monopole field",
"url": "https://arxiv.org/abs/quant-ph/9902034"
},
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