Algebraic integrability of ${\cal PT}$-deformed Calogero models

TL;DR

This paper reviews recent algebraic and spectral developments in non-Hermitian PT-deformed Calogero models, highlighting their integrability, symmetries, and regularization methods.

Contribution

It introduces algebraic integrability and PT-symmetry deformations in Calogero models, expanding understanding of their spectral properties and symmetries.

Findings

Identification of algebraic integrability at specific couplings

Analysis of intertwining operators and conserved charges

Physical regularization via PT-symmetry deformation

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 $A_2$ 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 $\mathcal{PT}$-symmetry deformation.