# On the composition of Berezin-Toeplitz operators on symplectic manifolds

## TL;DR

This paper calculates the second coefficient in the composition of Berezin-Toeplitz operators on symplectic manifolds, utilizing the full off-diagonal Bergman kernel expansion to advance understanding of their algebraic structure.

## Contribution

It provides a detailed computation of the second coefficient in Berezin-Toeplitz operator composition on symplectic manifolds, extending previous asymptotic analysis.

## Key findings

- Explicit formula for the second coefficient in operator composition
- Use of full off-diagonal Bergman kernel expansion
- Enhanced understanding of Berezin-Toeplitz algebra on symplectic manifolds

## Abstract

We compute the second coefficient of the composition of two Berezin-Toeplitz operators associated with the $\text{spin}^c$ Dirac operator on a symplectic manifold, making use of the full-off diagonal expansion of the Bergman kernel.