Publications at the Riemann Center
Nonlinear supersymmetry in the quantum Calogero model
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.
Details
- Organisation(s)
-
Quest: Centre for Quantum Engineering and Space-Time Research
Institute of Theoretical Physics
Riemann Center for Geometry and Physics
- External Organisation(s)
-
Centro de Estudios Científicos (CECs)
Universidad de Santiago de Chile
- Type
- Article
- Journal
- Journal of high energy physics
- Volume
- 2014
- ISSN
- 1126-6708
- Publication date
- 04.2014
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Nuclear and High Energy Physics
- Electronic version(s)
-
https://doi.org/10.1007/JHEP04(2014)151 (Access:
Open
)
