Weyl-Underhill-Emmrich quantization and the Stratonovich-Weyl quantizer

TL;DR

This paper examines Weyl-Underhill-Emmrich quantization and the Stratonovich-Weyl quantizer, highlighting axiomatic challenges and discussing quantization on the cylinder within this framework.

Contribution

It analyzes the axiomatic issues of the SW quantizer and explores quantization on the cylinder using WUE formalism.

Findings

Axiomatic definition of SW quantizer faces severe difficulties

Quantization on the cylinder is discussed within WUE formalism

Highlights limitations of current quantization approaches

Abstract

Weyl-Underhill-Emmrich (WUE) quantization and its generalization are considered. It is shown that an axiomatic definition of the Stratonovich-Weyl (SW) quantizer leads to severe difficulties. Quantization on the cylinder within the WUE formalism is discussed.