Deformation quantization with separation of variables of an endomorphism bundle

TL;DR

This paper develops a star product on the sections of an endomorphism bundle over a pseudo-Kaehler manifold, extending separation of variables and generalizing Gammelgaard's graph formula.

Contribution

It introduces a new star product on endomorphism bundle sections with separation of variables and generalizes existing graph-theoretic formulas.

Findings

Constructed a star product on endomorphism bundle sections.

Proved a generalized Gammelgaard's graph formula.

Extended separation of variables property to endomorphism bundles.

Abstract

Given a holomorphic Hermitian vector bundle and a star-product with separation of variables on a pseudo-Kaehler manifold, we construct a star product on the sections of the endomorphism bundle of the dual bundle which also has the appropriately generalized property of separation of variables. For this star product we prove a generalization of Gammelgaard's graph-theoretic formula.