Details
| Original language | English |
|---|---|
| Article number | 151 |
| Journal | Journal of high energy physics |
| Volume | 2014 |
| Issue number | 4 |
| Publication status | Published - 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.
Keywords
- Conformal and W symmetry, Extended supersymmetry, Integrable equations in physics
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
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In: Journal of high energy physics, Vol. 2014, No. 4, 151, 04.2014.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Nonlinear supersymmetry in the quantum Calogero model
AU - Correa, Francisco
AU - Lechtenfeld, Olaf
AU - Plyushchay, Mikhail
N1 - Copyright: Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2014/4
Y1 - 2014/4
N2 - 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.
AB - 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.
KW - Conformal and W symmetry
KW - Extended supersymmetry
KW - Integrable equations in physics
UR - http://www.scopus.com/inward/record.url?scp=84901389305&partnerID=8YFLogxK
U2 - 10.1007/JHEP04(2014)151
DO - 10.1007/JHEP04(2014)151
M3 - Article
AN - SCOPUS:84901389305
VL - 2014
JO - Journal of high energy physics
JF - Journal of high energy physics
SN - 1126-6708
IS - 4
M1 - 151
ER -