Details
| Original language | English |
|---|---|
| Article number | 095 |
| Journal | Proceedings of Science |
| Volume | 292 |
| Publication status | Published - 2016 |
| Event | Corfu Summer Institute 2016 "School and Workshops on Elementary Particle Physics and Gravity", CORFU 2016 - Corfu, Greece Duration: 31 Aug 2016 → 12 Sept 2016 |
Abstract
The rational Calogero model based on the An-1 root system is spherically reduced to a superintegrable angular model of a particle moving on Sn-2 subject to a very particular potential singular at the Weyl chamber walls. We review the computation of its energy spectrum (including the eigenstates), conserved charges and intertwining operators shifting the coupling constant by one. These models are deformed in a PT -symmetric manner by judicious complex coordinate transformations, which render the potential less singular. The PT deformation does not change the energy levels but in some cases adds a previously unphysical tower of states. For integral couplings this roughly doubles the previous degeneracy and allows for a conserved nonlinear supersymmetry-type charge. We illustrate the general constructions by presenting the details for the cases of A2 and A3 and point out open questions.
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In: Proceedings of Science, Vol. 292, 095, 2016.
Research output: Contribution to journal › Conference article › Research › peer review
}
TY - JOUR
T1 - Calogero, spherically reduced and PT-deformed
AU - Correa, Francisco
AU - Lechtenfeld, Olaf
N1 - Publisher Copyright: © Copyright owned by the author(s) under the terms of the Creative Commons. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2016
Y1 - 2016
N2 - The rational Calogero model based on the An-1 root system is spherically reduced to a superintegrable angular model of a particle moving on Sn-2 subject to a very particular potential singular at the Weyl chamber walls. We review the computation of its energy spectrum (including the eigenstates), conserved charges and intertwining operators shifting the coupling constant by one. These models are deformed in a PT -symmetric manner by judicious complex coordinate transformations, which render the potential less singular. The PT deformation does not change the energy levels but in some cases adds a previously unphysical tower of states. For integral couplings this roughly doubles the previous degeneracy and allows for a conserved nonlinear supersymmetry-type charge. We illustrate the general constructions by presenting the details for the cases of A2 and A3 and point out open questions.
AB - The rational Calogero model based on the An-1 root system is spherically reduced to a superintegrable angular model of a particle moving on Sn-2 subject to a very particular potential singular at the Weyl chamber walls. We review the computation of its energy spectrum (including the eigenstates), conserved charges and intertwining operators shifting the coupling constant by one. These models are deformed in a PT -symmetric manner by judicious complex coordinate transformations, which render the potential less singular. The PT deformation does not change the energy levels but in some cases adds a previously unphysical tower of states. For integral couplings this roughly doubles the previous degeneracy and allows for a conserved nonlinear supersymmetry-type charge. We illustrate the general constructions by presenting the details for the cases of A2 and A3 and point out open questions.
UR - http://www.scopus.com/inward/record.url?scp=85046110138&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:85046110138
VL - 292
JO - Proceedings of Science
JF - Proceedings of Science
M1 - 095
T2 - Corfu Summer Institute 2016 "School and Workshops on Elementary Particle Physics and Gravity", CORFU 2016
Y2 - 31 August 2016 through 12 September 2016
ER -