Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models

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 $\mathcal{P}\mathcal{T}$-symmetry deformation.

arXiv comment16 pages, 10 figures, contribution to the proceedings in the Journal of Physics: Conference Series

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