This paper is devoted to the use of half-form bundles in the symbolic calculus of Berezin–Toeplitz operators on Kähler manifolds. We state the Bohr–Sommerfeld conditions and relate them to the functional calculus of Toeplitz operators, a trace formula and the characteristic classes in deformation quantization. We also develop the symbolic calculus of Lagrangian sections, with the crucial estimates of the subprincipal terms.
"Symbolic calculus for Toeplitz operators with half-form." J. Symplectic Geom. 4 (2) 171 - 198, June 2006.