On representations of Lie algebras of a generalized Tavis-Cummings model

[摘要] Consider the Lie algebrasLr,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,K3andK4are real diagonal operators representing energy,K2=K1†, and the HamiltonianH=ω1K3+(ω1+ω2)K4+λ(t)(K1eiΦ+K2eiΦ)is a Hermitian operator. Matrix representations are discussed and faithful representations of least degree forLr,t ssatisfying the physical requirements are given for appropriate values ofr,s,t∈ℝ.

[学科分类] 应用数学