Abstract
The symmetries of the generalized Calogero model and its discrete version are related to the well-known unitary symmetries of the isotropic oscillator. The correspondence is provided by the Dunkl-operator deformation of the standard quantum momentum.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
T. Hakobyan, Phys. Rev. D 99, 105011 (2019).
A. Polychronakos, Phys. Rev. Lett. 69, 703 (1992).
L. Brink, T. Hansson, and M. Vasiliev, Phys. Lett. B 286, 109 (1992).
F. Calogero, J. Math. Phys. 10, 2191 (1969);
J. Math. Phys. 12, 419 (1971).
M. A. Olshanetsky and A. M. Perelomov, Phys. Rep. 94, 313 (1983);
A. P. Polychronakos, J. Phys. A 39, 12793 (2006).
C. F. Dunkl, Trans. Am. Math. Soc. 311, 167 (1989).
J. A. Minahan and A. P. Polychronakos, Phys. Lett. B 302, 265 (1993).
M. Feigin and T. Hakobyan, J. High Energy Phys. 1511, 107 (2015).
V. B. Kuznetsov, Phys. Lett. A 218, 212 (1996).
M. Feigin, Theor. Math. Phys. 135, 497 (2003).
F. Correa, T. Hakobyan, O. Lechtenfeld, and A. Nersessian, Phys. Rev. D 93, 125009 (2016).
D. Bernard, M. Gaudin, F. D. M. Haldane, and V. Pasquier, J. Phys. A 26, 5219 (1993).
O. Lechtenfeld, A. Nersessian, and V. Yeghikyan, Phys. Lett. A 374, 4647 (2010);
T. Hakobyan, A. Nersessian, and H. Shmavonyan, Phys. Rev. D 95, 025014 (2017).
P. Mathieu and Y. Xudous, J. Phys. A 34, 4197 (2001);
J. C. Talstra and F. D. M. Haldane, J. Phys. A 28, 2369 (1995).
A. Polychronakos, Phys. Rev. Lett. 70, 2329 (1993).
H. Frahm, J. Phys. A 26, L473 (1993).
F. Calogero, Lett. Nuvo Chim. 20, 251 (1977).
M. Feigin, O. Lechtenfeld, and A. Polychronakos, J. High Energy Phys. 1307, 162 (2013).
Funding
This work was performed within ICTP Affiliated Center program AF-04. S.V. was supported by the Regional Doctoral Program on Theoretical and Experimental Particle Physics sponsored by VolkswagenStiftung, Germany. T.H. was supported by the Armenian State Committee of Science Grant no. 18T-1C106.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Tigran Hakobyan, Seda Vardanyan Symmetry Algebra of Dynamical and Discrete Calogero Models. Phys. Part. Nuclei Lett. 17, 734–737 (2020). https://doi.org/10.1134/S1547477120050179
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1547477120050179