A Universal Formula for Deformation Quantization on K\"ahler Manifolds

TL;DR

This paper presents an explicit local formula for deformation quantization with separation of variables on K"ahler manifolds, using differential operators and combinatorial graphs, advancing the mathematical understanding of quantization procedures.

Contribution

It introduces a universal explicit formula for deformation quantization on K"ahler manifolds, utilizing combinatorial graph parametrization, which was not previously available.

Findings

Provides a local formula for deformation quantization

Uses combinatorial graphs to parametrize differential operators

Advances explicit methods in geometric quantization

Abstract

We give an explicit local formula for any formal deformation quantization, with separation of variables, on a K\"ahler manifold. The formula is given in terms of differential operators, parametrized by acyclic combinatorial graphs.