Quantization via Deformation of Prequantization

TL;DR

This paper introduces a new geometric approach to quantization using a Souriau bracket on a prequantum bundle, providing a deformation method that yields a genuine quantization of the phase space.

Contribution

It proposes the concept of a Souriau bracket and demonstrates how deforming the prequantum bundle along this bracket achieves phase space quantization.

Findings

Souriau bracket defined on prequantum circle bundle

Deformation along the bracket yields phase space quantization

Provides a geometric framework for quantization

Abstract

We introduce the notion of a "Souriau bracket" on a prequantum circle bundle $Y$ over a phase space $X$ and explain how a deformation of $Y$ in the direction of this bracket provides a genuine quantization of $X$.