On the composition of Berezin-Toeplitz operators on symplectic manifolds

We compute the second coefficient of the composition of two Berezin–Toeplitz operators associated with the spinc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {spin}^c$$\end{document} Dirac operator on a symplectic manifold, making use of the full-off diagonal expansion of the Bergman kernel.