Exhausting formal quantization procedures

TL;DR

This paper discusses stable formality quasi-isomorphisms in formal quantization, showing that each homotopy class has a representative that can be globalized, advancing the understanding of quantization procedures.

Contribution

It proves that every homotopy class of stable formality quasi-isomorphisms contains a globalization-compatible representative.

Findings

Every homotopy class admits a globalizable representative

Provides a brief exposition of stable formality quasi-isomorphisms

Advances the theory of formal quantization procedures

Abstract

In paper arXiv:1109.6031 the author introduced stable formality quasi-isomorphisms and described the set of its homotopy classes. This result can be interpreted as a complete description of formal quantization procedures. In this note we give a brief exposition of stable formality quasi-isomorphisms and prove that every homotopy class of stable formality quasi-isomorphisms contains a representative which admits globalization. This note is loosely based on the talk given by the author at the XXX Workshop on Geometric Methods in Physics in Bialowieza, Poland.