Toeplitz operators on symplectic manifolds

Xiaonan Ma (1) , George Marinescu (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 Mathematisches Institut

We study the Berezin-Toeplitz quantization on symplectic manifolds making use of the full off-diagonal asymptotic expansion of the Bergman kernel. We give also a characterization of Toeplitz operators in terms of their asymptotic expansion. The semi-classical limit properties of the Berezin-Toeplitz quantization for non-compact manifolds and orbifolds are also established.

Domaines: Géométrie différentielle [math.DG]; Variables complexes [math.CV]; Géométrie symplectique [math.SG]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Xiaonan Ma, George Marinescu. Toeplitz operators on symplectic manifolds. 2008. ⟨hal-00872365⟩