Algebraic integrability of PT -deformed Calogero models

Francisco Correa; Olaf Lechtenfeld

doi:10.1088/1742-6596/2038/1/012007

Algebraic integrability of PT -deformed Calogero models

Francisco Correa, Olaf Lechtenfeld

Institut für Theoretische Physik

Universidad Austral de Chile

Publikation: Beitrag in Fachzeitschrift › Konferenzaufsatz in Fachzeitschrift › Forschung › Peer-Review

Abstract

We review some recents developments of the algebraic structures and spectral properties of non-Hermitian deformations of Calogero models. The behavior of such extensions is illustrated by the A2 trigonometric and the D3 angular Calogero models. Features like intertwining operators and conserved charges are discussed in terms of Dunkl operators. Hidden symmetries coming from the so-called algebraic integrability for integral values of the coupling are addressed together with a physical regularization of their action on the states by virtue of a PT -symmetry deformation.

Originalsprache	Englisch
Aufsatznummer	012007
Fachzeitschrift	Journal of Physics: Conference Series
Jahrgang	2038
Ausgabenummer	1
DOIs	https://doi.org/10.1088/1742-6596/2038/1/012007
Publikationsstatus	Veröffentlicht - 25 Okt. 2021
Veranstaltung	Virtual Seminar Series on Pseudo-Hermitian Hamiltonians in Quantum Physics: PTSeminar 2020 - London, Virtual, Großbritannien / Vereinigtes Königreich Dauer: 5 März 2021 → 5 März 2021

ASJC Scopus Sachgebiete

Allgemeine Physik und Astronomie

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10.1088/1742-6596/2038/1/012007Lizenz: CC BY 3.0

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abstract = "We review some recents developments of the algebraic structures and spectral properties of non-Hermitian deformations of Calogero models. The behavior of such extensions is illustrated by the A2 trigonometric and the D3 angular Calogero models. Features like intertwining operators and conserved charges are discussed in terms of Dunkl operators. Hidden symmetries coming from the so-called algebraic integrability for integral values of the coupling are addressed together with a physical regularization of their action on the states by virtue of a PT -symmetry deformation.",

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note = "Funding Information: FC was partially supported by Fondecyt grant 1211356. OL has been supported by the Deutsche Forschungsgemeinschaft under grant LE 838/12 and by the COST Action MP1405 QSPACE. ; Virtual Seminar Series on Pseudo-Hermitian Hamiltonians in Quantum Physics, PTSeminar 2020 ; Conference date: 05-03-2021 Through 05-03-2021",

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AU - Lechtenfeld, Olaf

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N2 - We review some recents developments of the algebraic structures and spectral properties of non-Hermitian deformations of Calogero models. The behavior of such extensions is illustrated by the A2 trigonometric and the D3 angular Calogero models. Features like intertwining operators and conserved charges are discussed in terms of Dunkl operators. Hidden symmetries coming from the so-called algebraic integrability for integral values of the coupling are addressed together with a physical regularization of their action on the states by virtue of a PT -symmetry deformation.

AB - We review some recents developments of the algebraic structures and spectral properties of non-Hermitian deformations of Calogero models. The behavior of such extensions is illustrated by the A2 trigonometric and the D3 angular Calogero models. Features like intertwining operators and conserved charges are discussed in terms of Dunkl operators. Hidden symmetries coming from the so-called algebraic integrability for integral values of the coupling are addressed together with a physical regularization of their action on the states by virtue of a PT -symmetry deformation.

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