On Gammelgaard's formula for a star product with separation of variables

Abstract

We show that Gammelgaard's formula expressing a star product with separation of variables on a pseudo-Kaehler manifold in terms of directed graphs without cycles is equivalent to an inversion formula for an operator on a formal Fock space. We prove this inversion formula directly and thus offer an alternative approach to Gammelgaard's formula which gives more insight into the question why the directed graphs in his formula have no cycles.

29 pages, changes made in the last two sections

References in corpus (3)

• 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

Cited by in corpus (3)

• A Universal Construction of Universal Deformation Formulas, Drinfel'd Twists and their Positivity
• Weyl invariant polynomial and deformation quantization on Kahler manifolds
• Deformation quantization with separation of variables of an endomorphism bundle