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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TMF_2003_137_2_a1,
     author = {\'A. Ballesteros and O. Civitarese and F. J. Herranz and M. Reboiro},
     title = {Effective $su_q(2)$ {Models} and {Polynomial} {Algebras} for {Fermion-Boson} {Hamiltonians}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {165--175},
     publisher = {mathdoc},
     volume = {137},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_137_2_a1/}
}
TY  - JOUR
AU  - Á. Ballesteros
AU  - O. Civitarese
AU  - F. J. Herranz
AU  - M. Reboiro
TI  - Effective $su_q(2)$ Models and Polynomial Algebras for Fermion-Boson Hamiltonians
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2003
SP  - 165
EP  - 175
VL  - 137
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2003_137_2_a1/
LA  - ru
ID  - TMF_2003_137_2_a1
ER  - 
%0 Journal Article
%A Á. Ballesteros
%A O. Civitarese
%A F. J. Herranz
%A M. Reboiro
%T Effective $su_q(2)$ Models and Polynomial Algebras for Fermion-Boson Hamiltonians
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2003
%P 165-175
%V 137
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2003_137_2_a1/
%G ru
%F TMF_2003_137_2_a1
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/