On representations of Lie algebras of a generalized Tavis-Cummings model
Consider the Lie algebras Lr,t s:[K1,K2]=sK3, [K3,K1]=rK1, [K3,K2]=−rK2, [K3,K4]=0, [K4,K1]=−tK1, and [K4,K2]=tK2, subject to the physical conditions, K3 and K4 are real diagonal operators representing energy, K2=K1†, and the Hamiltonian H=ω1K3+(ω1+ω2)K4+λ(t)(K1eiΦ+K2eiΦ) is a Hermitian operator. Ma...
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Hindawi Limited
2003-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X03202047 |
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doaj-964a60d9989b42d4baf4ef7bac316f8a2020-11-24T22:55:54ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422003-01-0120031556410.1155/S1110757X03202047On representations of Lie algebras of a generalized Tavis-Cummings modelL. A. M. Hanna0Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, P.O. Box 5969, Safat 13060, KuwaitConsider the Lie algebras Lr,t s:[K1,K2]=sK3, [K3,K1]=rK1, [K3,K2]=−rK2, [K3,K4]=0, [K4,K1]=−tK1, and [K4,K2]=tK2, subject to the physical conditions, K3 and K4 are real diagonal operators representing energy, K2=K1†, and the Hamiltonian H=ω1K3+(ω1+ω2)K4+λ(t)(K1eiΦ+K2eiΦ) is a Hermitian operator. Matrix representations are discussed and faithful representations of least degree for Lr,t s satisfying the physical requirements are given for appropriate values of r,s,t∈ℝ.http://dx.doi.org/10.1155/S1110757X03202047 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
L. A. M. Hanna |
| spellingShingle |
L. A. M. Hanna On representations of Lie algebras of a generalized Tavis-Cummings model Journal of Applied Mathematics |
| author_facet |
L. A. M. Hanna |
| author_sort |
L. A. M. Hanna |
| title |
On representations of Lie algebras of a generalized Tavis-Cummings model |
| title_short |
On representations of Lie algebras of a generalized Tavis-Cummings model |
| title_full |
On representations of Lie algebras of a generalized Tavis-Cummings model |
| title_fullStr |
On representations of Lie algebras of a generalized Tavis-Cummings model |
| title_full_unstemmed |
On representations of Lie algebras of a generalized Tavis-Cummings model |
| title_sort |
on representations of lie algebras of a generalized tavis-cummings model |
| publisher |
Hindawi Limited |
| series |
Journal of Applied Mathematics |
| issn |
1110-757X 1687-0042 |
| publishDate |
2003-01-01 |
| description |
Consider the Lie algebras Lr,t s:[K1,K2]=sK3, [K3,K1]=rK1, [K3,K2]=−rK2, [K3,K4]=0, [K4,K1]=−tK1, and [K4,K2]=tK2, subject to the physical conditions, K3 and K4 are real diagonal operators representing energy, K2=K1†, and the Hamiltonian H=ω1K3+(ω1+ω2)K4+λ(t)(K1eiΦ+K2eiΦ) is a Hermitian operator. Matrix representations are discussed and faithful representations of least degree for Lr,t s satisfying the physical requirements are given for appropriate values of r,s,t∈ℝ. |
| url |
http://dx.doi.org/10.1155/S1110757X03202047 |
| work_keys_str_mv |
AT lamhanna onrepresentationsofliealgebrasofageneralizedtaviscummingsmodel |
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