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

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.