The SPIN${}^c$ Dirac operator on high tensor powers of a line bundle

Abstract

We study the asymptotic of the spectrum of the \spin Dirac operator on high tensor powers of a line bundle. As application, we get a simple proof of the main result of Guillemin-Uribe, which was originally proved by using the analysis of Toeplitz operators of Boutet de Monvel and Guillemin.

Math. Zeitschrift, to appear

Cited by in corpus (23)

• Generalized Bergman kernels on symplectic manifolds
• On the asymptotic expansion of Bergman kernel
• Toeplitz operators on symplectic manifolds
• Exponential Estimate for the asymptotics of Bergman kernels
• Geometric quantization for proper actions
• The first coefficients of the asymptotic expansion of the Bergman kernel of the spin^c Dirac operator
• Bochner Laplacian and Bergman kernel expansion of semi-positive line bundles on a Riemann surface
• Remarks on the naturality of quantization
• Generalized Bergman kernels on symplectic manifolds of bounded geometry
• Semi-classical properties of Berezin--Toeplitz operators with $\cC^k$--\,symbol
• Donaldson's $Q$-operators for symplectic manifolds
• The matrix regularization for Riemann surfaces with magnetic fluxes
• Semiclassical spectral analysis of Toeplitz operators on symplectic manifolds: the case of discrete wells
• On the spectrum of non degenerate magnetic Laplacian
• Laplacians on Fuzzy Riemann Surfaces
• Cohomology dimension growth for Nakano $q$-semipositive line bundles
• A semiclassical Birkhoff normal form for constant-rank magnetic fields
• The first terms in the expansion of the Bergman kernel in higher degrees
• Diffeomorphisms on Fuzzy Sphere
• Quantization, dequantization, and distinguished states
• Geometric quantization of Hamiltonian flows and the Gutzwiller trace formula
• Geometric quantization of symplectic maps and Witten's asymptotic conjecture
• The spectral density function of the renormalized Bochner Laplacian on a symplectic manifold