Quantization of Calogero-Painlev\'e System and Multi-Particle Quantum Painlev\'e Equations II-VI
Mathematical Physics
2021-09-08 v2 math.MP
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.2103.09681,
title = {Quantization of Calogero-Painlev\'e System and Multi-Particle Quantum Painlev\'e Equations II-VI},
author = {Fatane Mobasheramini and Marco Bertola},
journal= {arXiv preprint arXiv:2103.09681},
year = {2021}
}