Vector coherent state theory of the generic representations of so ( 5 ) in an so ( 3 ) basis
For applications of group theory in quantum mechanics, one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some Hamiltonian of interest. Here we use vector coherent state techniques to develop an algorithm for...
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| Veröffentlicht in: | Journal of mathematical physics 2006-02, Vol.47 (2), p.023507-023507-25 |
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| container_end_page | 023507-25 |
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| container_issue | 2 |
| container_start_page | 023507 |
| container_title | Journal of mathematical physics |
| container_volume | 47 |
| creator | Turner, P. S. Rowe, D. J. Repka, J. |
| description | For applications of group theory in quantum mechanics, one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some Hamiltonian of interest. Here we use vector coherent state techniques to develop an algorithm for constructing the matrices for arbitrary finite-dimensional irreps of the SO(5) Lie algebra in an SO(3) basis. The SO(3) subgroup of SO(5) is defined by regarding SO(5) as linear transformations of the five-dimensional space of an SO(3) irrep of angular momentum two. A need for such irreps arises in the nuclear collective model of quadrupole vibrations and rotations. The algorithm has been implemented in MAPLE, and some tables of results are presented. |
| doi_str_mv | 10.1063/1.2162332 |
| format | Article |
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S.</creatorcontrib><creatorcontrib>Rowe, D. J.</creatorcontrib><creatorcontrib>Repka, J.</creatorcontrib><title>Vector coherent state theory of the generic representations of so ( 5 ) in an so ( 3 ) basis</title><title>Journal of mathematical physics</title><description>For applications of group theory in quantum mechanics, one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some Hamiltonian of interest. Here we use vector coherent state techniques to develop an algorithm for constructing the matrices for arbitrary finite-dimensional irreps of the SO(5) Lie algebra in an SO(3) basis. The SO(3) subgroup of SO(5) is defined by regarding SO(5) as linear transformations of the five-dimensional space of an SO(3) irrep of angular momentum two. A need for such irreps arises in the nuclear collective model of quadrupole vibrations and rotations. 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J.</au><au>Repka, J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Vector coherent state theory of the generic representations of so ( 5 ) in an so ( 3 ) basis</atitle><jtitle>Journal of mathematical physics</jtitle><date>2006-02-01</date><risdate>2006</risdate><volume>47</volume><issue>2</issue><spage>023507</spage><epage>023507-25</epage><pages>023507-023507-25</pages><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>For applications of group theory in quantum mechanics, one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some Hamiltonian of interest. Here we use vector coherent state techniques to develop an algorithm for constructing the matrices for arbitrary finite-dimensional irreps of the SO(5) Lie algebra in an SO(3) basis. 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| identifier | ISSN: 0022-2488 |
| ispartof | Journal of mathematical physics, 2006-02, Vol.47 (2), p.023507-023507-25 |
| issn | 0022-2488 1089-7658 |
| language | eng |
| recordid | cdi_scitation_primary_10_1063_1_2162332 |
| source | AIP Journals Complete; AIP Digital Archive |
| subjects | ALGEBRA ALGORITHMS ANGULAR MOMENTUM ANNIHILATION OPERATORS CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS COLLECTIVE MODEL EIGENSTATES Exact sciences and technology GROUP THEORY HAMILTONIANS Mathematical methods in physics Mathematics MATRICES Physics QUADRUPOLES QUANTUM MECHANICS ROTATION Sciences and techniques of general use SO-3 GROUPS SO-5 GROUPS SPECTRA TRANSFORMATIONS VECTORS |
| title | Vector coherent state theory of the generic representations of so ( 5 ) in an so ( 3 ) basis |
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