Quantisation ideals of nonabelian integrable systems

TL;DR

This paper introduces a new approach to quantising nonabelian integrable systems by defining quantisation ideals, with examples demonstrating the method's applicability to systems with infinite-dimensional symmetry algebras.

Contribution

It proposes the concept of quantisation ideals for nonabelian integrable systems, offering a novel framework for their quantisation.

Findings

Defined the concept of quantisation ideals.

Provided meaningful examples illustrating the approach.

Established a new framework for quantising systems with infinite symmetries.

Abstract

We consider dynamical systems on the space of functions taking values in a free associative algebra. The system is said to be integrable if it possesses an infinite dimensional Lie algebra of commuting symmetries. In this paper we propose a new approach to the problem of quantisation of dynamical systems, introduce the concept of quantisation ideals and provide meaningful examples.