Volume 292 - Corfu Summer Institute 2016 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2016) - Workshop on Geometry and Physics, Ringberg Castle, 20-25 November 2016, invited contributions
Calogero, spherically reduced and PT-deformed
F. Correa and O. Lechtenfeld*
Full text: pdf
Pre-published on: October 04, 2017
Published on: October 05, 2017
Abstract
The rational Calogero model based on the $A_{n-1}$ root system is spherically reduced to a superintegrable angular model of a particle moving on $S^{n-2}$ 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 ${\cal PT}$-symmetric manner by judicious complex coordinate transformations, which render the potential less singular. The ${\cal PT}$ 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 $A_2$ and $A_3$ and point out open questions.
DOI: https://doi.org/10.22323/1.292.0095
How to cite

Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.

Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.