Quantization of Poisson-Hamiltonian systems

TL;DR

This paper explores the quantization of Hamiltonian systems within the Poisson framework, employing formal deformation quantization and quantum group theories to extend classical mechanics into quantum regimes.

Contribution

It introduces a novel approach to quantizing Poisson-Hamiltonian systems using deformation quantization and quantum groups, bridging classical and quantum mechanics.

Findings

Developed a formal deformation quantization method for Poisson-Hamiltonian systems.

Applied quantum group theories to the quantization process.

Provided a framework connecting classical Poisson systems with quantum structures.

Abstract

In this paper we introduce the concept of Hamiltonian system in the canonical and Poisson settings. We will discuss the quantization of the Hamiltonian systems in the Poisson context, using formal deformation quantization and quantum group theories.