Journal of Applied Mathematics
Volume 2003 (2003), Issue 1, Pages 55-64
doi:10.1155/S1110757X03202047
On representations of Lie algebras of a generalized Tavis-Cummings model
Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
Received 13 February 2002; Revised 9 July 2002
Copyright © 2003 L. A. M. Hanna. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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.