Geometrical framework of quantization problem

TL;DR

This paper reviews the geometric approach to quantization, connecting classical methods, Lie group representations, and the potential link between quantization and discretization of space.

Contribution

It summarizes the geometric formalism of quantization and explores the relationship between quantization and discretization of the configuration space.

Findings

Highlights the geometric formalism in quantization

Discusses the link between quantization and space discretization

Connects classical quantum mechanics with Lie group representations

Abstract

The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship between quantization and discretization of the configuration space is briefly discussed.