Geodesic
Effective $su_q(2)$ Models and Polynomial Algebras for Fermion-Boson Hamiltonians
Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 2, pp. 165-175 Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that schematic $su(2)\oplus h_3$ interaction Hamiltonians, where $su(2)$ plays the role of the pseudospin algebra of fermion operators and $h_3$ is the Heisenberg algebra for bosons, are closely related to certain nonlinear models defined on a single quantum algebra $su_q(2)$ of quasifermions. In particular, $su_q(2)$ analogues of the Da Providencia–Schütte and extended Lipkin models are presented. We analyze the connection between $q$ and the physical parameters of the fermion-boson system and, using polynomial algebras, discuss the integrability properties of the interaction Hamiltonians.
Keywords: quantum algebras, effective Hamiltonians, dynamical symmetry, nuclear physics. 
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Á. Ballesteros; O. Civitarese; F. J. Herranz; M. Reboiro. Effective $su_q(2)$ Models and Polynomial Algebras for Fermion-Boson Hamiltonians. Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 2, pp. 165-175. http://geodesic.mathdoc.fr/item/TMF_2003_137_2_a1/

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