Deformation quantization with separation of variables of an endomorphism bundle

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.

29 pages, an important reference is added, several typos corrected

References in corpus (4)

• An explicit formula for the Berezin star product
• A Universal Formula for Deformation Quantization on Kähler Manifolds
• On a formula of Gammelgaard for Berezin-Toeplitz quantization
• On Gammelgaard's formula for a star product with separation of variables

Cited by in corpus (1)

• Weyl invariant polynomial and deformation quantization on Kahler manifolds