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

Abstract

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.

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• Viscous shocks in Hele-Shaw flow and Stokes phenomena of the Painleve I transcendent
• From topological recursion to wave functions and PDEs quantizing hyperelliptic curves