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

• Published in: International journal of mathematics and mathematical sciences Vol. 2022; pp. 1 - 8
• Main Authors: Hanna, Latif A -M., Alazemi, Abdullah, Al-Dhafeeri, Anwar
• Format: Journal Article
• Language: English
• Published: New York Hindawi 19.09.2022; John Wiley & Sons, Inc; Wiley
• Subjects: Algebra; Analysis; Conjugation; Deformation; Lie groups; Matrix representation; Operators (mathematics); Optics; Oscillators; Partial differential equations; Physical properties; Quantum optics; Radiation; Iran
• ISSN: 0161-1712; 1687-0425
• DOI: 10.1155/2022/6737287

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∈ℝ−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 alg...