A Product Expansion for Toeplitz Operators on the Fock Space

TL;DR

This paper develops an improved asymptotic expansion for the product of Toeplitz operators on the Fock space, requiring fewer derivatives and achieving arbitrary order, thereby advancing Toeplitz quantization methods.

Contribution

It introduces a more efficient asymptotic expansion for Toeplitz operator products on the Fock space with fewer derivatives and arbitrary order, improving previous results.

Findings

Derived an asymptotic expansion requiring fewer derivatives

Achieved expansion to arbitrary order

Established an intertwining identity between Berezin star and sharp products

Abstract

We study the asymptotic expansion of the product of two Toeplitz operators on the Fock space. In comparison to earlier results we require significantly less derivatives and get the expansion to arbitrary order. This, in particular, improves a result of Borthwick related to Toeplitz quantization. In addition, we derive an intertwining identity between the Berezin star product and the sharp product.