An explicit formula for the Berezin star product

TL;DR

This paper derives an explicit combinatorial formula for the Berezin star product on Kähler manifolds, linking geometric quantization with graph theory and asymptotic analysis.

Contribution

It provides the first explicit formula for the Berezin star product expressed as a sum over strongly connected digraphs, based on combinatorial and asymptotic methods.

Findings

Explicit formula for Berezin star product using digraphs

Connection between geometric quantization and combinatorics

Proof relies on asymptotic expansion of Laplace integrals

Abstract

We prove an explicit formula of the Berezin star product on Kaehler manifolds. The formula is expressed as a summation over certain strongly connected digraphs. The proof relies on a combinatorial interpretation of Englis' work on the asymptotic expansion of the Laplace integral.