Open AccessAlgebraic integrability of PT -deformed Calogero models
Author(s) -
Francisco Correa,
Olaf Lechtenfeld
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2038/1/012007
Subject(s) - homogeneous space , algebraic number , trigonometry , trigonometric functions , pure mathematics , hermitian matrix , regularization (linguistics) , mathematics , algebra over a field , mathematical physics , mathematical analysis , computer science , geometry , artificial intelligence
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 A 2 trigonometric and the D 3 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.