Spectral convergence in geometric quantization -- the case of non-singular Langrangian fibrations

Abstract

We develop a new approach to geometric quantization using the theory of convergence of metric measure spaces. Given a family of Kähler polarizations converging to a non-singular real polarization on a prequantized symplectic manifold, we show the spectral convergence result of $\bar{\partial }$-Laplacians, as well as the convergence result of quantum Hilbert spaces. We also consider the case of almost Kähler quantization for compatible almost complex structures, and show the analogous convergence results.

To appear in The Journal of Symplectic Geometry

References in corpus (3)

• The Joint Spectral Flow and Localization of the Indices of Elliptic Operators
• Spectral convergence in geometric quantization --- the case of toric symplectic manifolds
• Spectral convergence in geometric quantization on $K3$ surfaces

Cited by in corpus (2)

• Spectral convergence in geometric quantization --- the case of toric symplectic manifolds
• Spectral convergence in geometric quantization on $K3$ surfaces