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arXiv · 2103.09681

Quantization of Calogero-Painlev\'e System and Multi-Particle Quantum Painlev\'e Equations II-VI

Fatane Mobasheramini·Marco Bertola
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Abstract

We consider the isomonodromic formulation of the Calogero-Painlev\'e 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 Painlev\'e equations. We also provide multi-particle generalizations of these integral representations.

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Fatane Mobasheramini, Marco Bertola. 2021-03-17. Quantization of Calogero-Painlev\'e System and Multi-Particle Quantum Painlev\'e Equations II-VI. https://doi.org/10.3842/sigma.2021.081

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