Nonlinear supersymmetry in the quantum Calogero model

authored by

Francisco Correa, Olaf Lechtenfeld, Mikhail Plyushchay

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.

Organisation(s)

Quest: Centre for Quantum Engineering and Space-Time Research
Institut für Theoretische Physik
Riemann Center for Geometry and Physics

External Organisation(s)

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

Type

Artikel

Journal

Journal of high energy physics

Volume

2014

ISSN

1126-6708

Publication date

04.2014

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Kern- und Hochenergiephysik

Electronic version(s)

https://doi.org/10.1007/JHEP04(2014)151 (Access: Offen)