  The so-called quantization problem in geometric quantization is asking
whether the space of wave functions is independent of the choice of
polarization. In this paper, we apply SYZ transforms to solve the quantization
problem in two cases: (1) semi-flat Lagrangian torus fibrations over complete
compact integral affine manifolds, and (2) projective toric manifolds. More
precisely, we prove that the space of wave functions associated to the real
polarization is canonically isomorphic to that associated to a complex
polarization via SYZ transforms in both cases.

Symplectic Geometry