Quantization of classical integrable systems. Part II: quantization of functions on Poisson manifolds

TL;DR

This paper explores conditions for quantizing classical integrable systems into quasi-integrable quantum systems using symmetrized operator products, laying groundwork for future applications.

Contribution

It establishes sufficient conditions for quantizing classical integrable systems into quasi-integrable quantum systems via symmetrized products.

Findings

Identifies conditions for successful quantization of integrable systems

Framework for constructing quasi-integrable quantum systems

Prepares for application to specific classes of systems in future work

Abstract

In a previous work we have introduced the concept of quasi-integrable quantum system. In the present one we determine sufficient conditions under which, given an integrable classical system, it is possible to construct a quasi-integrable quantum system by means of a quantization procedure based on the symmetrized product of operators. This procedure will be applied to concrete classes of integrable systems in two following papers.