On wave functions in geometric quantization

Antonio Díaz Miranda

V. P. Nair

Abstract This chapter gives the basic framework of geometric quantization. Prequantum operators, polarization and the integration measures for the inner product of wave functions are introduced.

Jędrzej Śniatycki

Jędrzej Śniatycki

MODUGNO M., TEJERO PRIETO C., Raffaele Vitolo

In this paper we review our results on the quantization of a rigid body. The fact that the configuration space is not simply connected yields two inequivalent quantizations. One of the quantizations allows us to recover classically double-valued wave functions as single valued sections of a non-trivial complex line bundle. This reopens the problem of a physical interpretation of these wave functions.

José M. Gracia-Bondía, Joseph C. Várilly

It is shown how the Moyal product of phase-space functions, and the Weyl correspondence between symbols and operator kernels, may be obtained directly using the procedures of geometric quantization, applied to the symplectic groupoid constructed by ‘‘doubling’’ the phase space.