Remarks on the naturality of quantization

Abstract

Hamiltonian quantization of an integral compact symplectic manifold M depends on a choice of compatible almost complex structure J. For open sets U in the set of compatible almost complex structures and small enough values of Planck's constant, the Hilbert spaces of the quantization form a bundle over U with a natural connection. In this paper we examine the dependence of the Hilbert spaces on the choice of J, by computing the semi-classical limit of the curvature of this connection. We also show that parallel transport provides a link between the action of the group Symp(M) of symplectomorphisms of M and the Schrodinger equation.

20 pages

References in corpus (3)

• Generalized Bergman kernels on symplectic manifolds
• Semi-classical properties of geometric quantization with metaplectic correction
• Geometric Quantization, Parallel Transport and the Fourier Transform

Cited by in corpus (6)

• Quantization of compact Riemannian symmetric spaces
• On a quasimorphism of Hamiltonian diffeomorphisms and quantization
• Toeplitz Operators, Kähler Manifolds, and Line Bundles
• Geometric quantization of Hamiltonian flows and the Gutzwiller trace formula
• Geometric quantization of symplectic maps and Witten's asymptotic conjecture
• The formal moment map geometry of the space of symplectic connections