Nonlinear supersymmetry in the quantum Calogero model

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Correa, F.; Lechtenfeld, O.; Plyushchay, M.: Nonlinear supersymmetry in the quantum Calogero model. In: Journal of High Energy Physics 2014 (2014), Nr. 4, 151. DOI: https://doi.org/10.1007/JHEP04(2014)151

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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.
License of this version: CC BY 4.0
Document Type: article
Publishing status: publishedVersion
Issue Date: 2014
Appears in Collections:Fakultät für Mathematik und Physik

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1 image of flag of Germany Germany 39 97.50%
2 image of flag of India India 1 2.50%

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