Normalized Weyl-type $\star$-product on K\"ahler manifolds

TL;DR

This paper introduces a normalized Weyl-type star product on Kähler manifolds, demonstrating that it simplifies the first-order expansion by removing a cumbersome term present in Berezin-type products, thus eliminating the need for a normalization factor at that order.

Contribution

The paper develops a normalized Weyl-type star product on Kähler manifolds and shows it simplifies first-order expansions by avoiding the normalization factor used in Berezin-type products.

Findings

Cumbersome term absent at first order in the Weyl-type product

Normalization factor unnecessary at first order for the Weyl-type product

Simplifies deformation quantization on Kähler manifolds

Abstract

We define a normalized Weyl-type $\star$-product on general K\"{a}hler manifolds. Expanding this product perturbatively we show that the cumbersome term, which appears in a Berezin-type product, does not appear at least in the first order of $\hbar$. This means a normalization factor, which is introduced by Reshetikhin and Takhtajan for a Berezin-type product, is unnecessary for our Weyl-type product at that order.