Quantization of Calogero–Painlevé System and Multi-Particle Quantum Painlevé Equations II–VI

Fatane Mobasheramini ; Marco Bertola

Symmetry, integrability and geometry: methods and applications, Tome 17 (2021)

Résumé

We consider the isomonodromic formulation of the Calogero–Painlevé multi-particle systems and proceed to their canonical quantization. We then proceed to the quantum Hamiltonian reduction on a special representation to radial variables, in analogy with the classical case and also with the theory of quantum Calogero equations. This quantized version is compared to the generalization of a result of Nagoya on integral representations of certain solutions of the quantum Painlevé equations. We also provide multi-particle generalizations of these integral representations.

Détail

Keywords: Harish-Chandra isomorphism.
Mots-clés : quantization of Painlevé, Calogero–Painlevé

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