Quantization of the Momentum Map via $\frak{g}$-adapted Formalities

TL;DR

This paper proves the existence and classifies $G$-invariant star products with quantum momentum maps on Poisson manifolds using an equivariant formality theorem, advancing the understanding of deformation quantization.

Contribution

It introduces an equivariant formality theorem to classify and establish the existence of $G$-invariant star products with quantum momentum maps.

Findings

Complete classification of $G$-invariant star products

Proof of existence of such star products

Application of equivariant formality theorem

Abstract

In this note, we provide a proof of the existence and complete classification of $G$-invariant star products with quantum momentum maps on Poisson manifolds by means of an equivariant version of the formality theorem.