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

L. A. M. Hanna

Journal of Applied Mathematics, 2003, vol. 2003, issue 1, 55-64

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.

Date: 2003
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https://doi.org/10.1155/S1110757X03202047

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2003:y:2003:i:1:p:55-64

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