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

L. A. M. Hanna

Journal of Applied Mathematics, 2003, vol. 2003, 1-10

Abstract:

Consider the Lie algebras L r , t   s : [ K 1 , K 2 ] = s K 3 , [ K 3 , K 1 ] = r K 1 , [ K 3 , K 2 ] = − r K 2 , [ K 3 , K 4 ] = 0 , [ K 4 , K 1 ] = − t K 1 , and [ K 4 , K 2 ] = t K 2 , subject to the physical conditions, K 3 and K 4 are real diagonal operators representing energy, K 2 = K 1 †, and the Hamiltonian H = ω 1 K 3 + ( ω 1 + ω 2 ) K 4 + λ ( t ) ( K 1 e i Φ + K 2 e i Φ ) is a Hermitian operator. Matrix representations are discussed and faithful representations of least degree for L r , t   s satisfying the physical requirements are given for appropriate values of r , s , t ∈ ℠.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:927451

DOI: 10.1155/S1110757X03202047

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