On representations of Lie algebras of a generalized Tavis-Cummings model
Hanna, L. A. M.
J. Appl. Math., Tome 2003 (2003) no. 1, p. 55-64 / Harvested from Project Euclid
Consider the Lie algebras $L_{r,t}^{s}:[ K_{1},K_{2}] = sK_{3}$ , $[K_{3},K_{1}] = rK_{1}$ , $[K_{3},K_{2}] = -rK_{2}$ , $[K_{3},K_{4}] = 0$ , $[K_{4},K_{1}] = -tK_{1}$ , and $[K_{4},K_{2}] = tK_{2}$ , subject to the physical conditions, $K_3$ and $K_4$ are real diagonal operators representing energy, $K_2 = K_{1}^{\dagger}$ , and the Hamiltonian $H =\omega_{1}K_{3} + (\omega_{1}+\omega_{2})K_{4} +\lambda(t)(K_{1}e^{-i\phi}+K_{2}e^{i\phi})$ 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 $r,s,t\in\mathbb{R}$ .
Publié le : 2003-01-23
Classification:  17B10,  17B81,  15A90,  35Q40,  81V80
@article{1049725680,
     author = {Hanna, L. A. M.},
     title = {On representations of Lie algebras of a generalized Tavis-Cummings model},
     journal = {J. Appl. Math.},
     volume = {2003},
     number = {1},
     year = {2003},
     pages = { 55-64},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1049725680}
}
Hanna, L. A. M. On representations of Lie algebras of a generalized Tavis-Cummings model. J. Appl. Math., Tome 2003 (2003) no. 1, pp.  55-64. http://gdmltest.u-ga.fr/item/1049725680/