Symbolic calculus for Toeplitz operators with half-form

Abstract

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.