The scalar curvature in formal deformation quantization. I

TL;DR

This paper explores the use of formal deformation quantization to connect scalar curvature with moment map constructions, extending classical geometric concepts into a quantum framework.

Contribution

It introduces a formal moment map construction on almost complex structures that generalizes the Donaldson-Fujiki moment map for scalar curvature.

Findings

Recovering the classical moment map in the integrable case

Deforming the scalar curvature moment map through formal deformation

Establishing a link between scalar curvature and quantum deformation concepts

Abstract

In the framework of formal deformation quantization, we apply our formal moment map construction on the space of almost complex structures to recover the Donaldson-Fujiki moment map picture of the Hermitian scalar curvature. In the integrable case, it yields a formal moment map deforming the scalar curvature moment map.