Nonlinear supersymmetry in the quantum Calogero model

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  • Centro de Estudios Científicos (CECs)
  • Universidad de Santiago de Chile
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Details

OriginalspracheEnglisch
Aufsatznummer151
FachzeitschriftJournal of high energy physics
Jahrgang2014
Ausgabenummer4
PublikationsstatusVeröffentlicht - Apr. 2014

Abstract

It is long known that the rational Calogero model describing n identical particles on a line with inverse-square mutual interaction potential is quantum superintegrable. We review the (nonlinear) algebra of the conserved quantum charges and the intertwiners which relate the Liouville charges at couplings g and g1. For integer values of g, these intertwiners give rise to additional conserved charges commuting with all Liouville charges and known since the 1990s. We give a direct construction of such a charge, the unique one being totally antisymmetric under particle permutations. It is of order 1 2n(n1)(2g1) in the momenta and squares to a polynomial in the Liouville charges. With a natural Z2 grading, this charge extends the algebra of conserved charges to a nonlinear supersymmetric one. We provide explicit expressions for intertwiners, charges and their algebra in the cases of two, three and four particles.

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Nonlinear supersymmetry in the quantum Calogero model. / Correa, Francisco; Lechtenfeld, Olaf; Plyushchay, Mikhail.
in: Journal of high energy physics, Jahrgang 2014, Nr. 4, 151, 04.2014.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Correa F, Lechtenfeld O, Plyushchay M. Nonlinear supersymmetry in the quantum Calogero model. Journal of high energy physics. 2014 Apr;2014(4):151. doi: 10.1007/JHEP04(2014)151
Correa, Francisco ; Lechtenfeld, Olaf ; Plyushchay, Mikhail. / Nonlinear supersymmetry in the quantum Calogero model. in: Journal of high energy physics. 2014 ; Jahrgang 2014, Nr. 4.
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