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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2003-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X03202047 |
| Summary: | 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. |
|---|---|
| ISSN: | 1110-757X 1687-0042 |