On Faithful Matrix Representations of q-Deformed Models in Quantum Optics

Latif A -M. Hanna, Abdullah Alazemi, Anwar Al-Dhafeeri and Maria A. Lledo

International Journal of Mathematics and Mathematical Sciences, 2022, vol. 2022, 1-8

Abstract: Consider the q-deformed Lie algebra, tq:K^1,K^2q=1−qK^1K^2,K^3,K^1q=sK^3, K^1,K^4q=sK^4,K^3,K^2q=tK^3,K^2,K^4q=tK^4, and K^4,K^3q=rK^1, where r,s,t∈℠−0, subject to the physical properties: K^1 and K^2 are real diagonal operators, and K^3=K^4†, (†is for Hermitian conjugation). The q-deformed Lie algebra, tq is introduced as a generalized model of the Tavis–Cummings model (Tavis and Cummings 1968, Bashir and Sebawe Abdalla 1995), namely, K^1,K^2=0,K^1,K^3=−2K^3,K^1,K^4=2K^4,K^2,K^3=K^3,K^2,K^4=K^4, and K^4,K^3=K^1, which is subject to the physical properties K^1 and K^2 are real diagonal operators, and K^3=K^4†. Faithful matrix representations of the least degree of tq are discussed, and conditions are given to guarantee the existence of the faithful representations.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:6737287

DOI: 10.1155/2022/6737287

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