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

Francisco Correa; Olaf Lechtenfeld

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arXiv · 2106.05428

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

Francisco Correa·Olaf Lechtenfeld

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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 $A_2$ 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.

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hep-th math-ph math.MP nlin.SI

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Francisco Correa, Olaf Lechtenfeld. 2021-06-09. Algebraic integrability of ${\cal PT}$-deformed Calogero models. https://arxiv.org/abs/2106.05428

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