On Certain Quantization Aspects of (Generalized) Toda Systems

TL;DR

This paper investigates the quantization of Toda systems and their hierarchies using canonical transformations, Lax pairs, and approaches like deformation quantization and quantum groups, highlighting new insights into their quantum properties.

Contribution

It introduces a novel analysis of quantization methods applied to generalized Toda systems and their hierarchies, including the use of quantum transformations and Lax pair frameworks.

Findings

Quantization of Toda systems via canonical and Poisson transformations.

Development of a hierarchy of quantized Toda systems using Lax pairs.

Discussion of quantum aspects with deformation quantization and quantum groups.

Abstract

Ordinary and gl(n,R) generalized Toda systems as well as a related hierarchy are probed with respect to certain quantization characteristics. "Quantum" canonical and Poisson transformations are used to study quantizations of transformed Toda systems. With a Lax pair setting, a hierarchy of related systems are shown and their quantizations discussed. Finally, comments are added about quantum aspects of gl(n,R) generalized Toda systems with the approaches of deformation quantization or quantum groups in mind.