I will review the Kostant-Souriau geometric quantization procedure for passing from functions on a symplectic manifold (classical observables) to operators on a Hilbert space (quantum observables). With the "half-form correction" that is required in this procedure, one cannot quantize a complex projective space of even complex dimension, and one cannot equivariantly quantize the two-sphere nor any symplectic toric manifold. I will present a geometric quantization procedure that uses metaplectic-c structures to incorporate the half-form correction into the earlier prequantization stage and that does apply to these examples. This follows work of Harald Hess from the late 1970s with recent contributions of Jennifer Vaughan.
Tue, 15/05/2018 - 12:00 to 13:30
Room 110, Manchester Buildling, Jerusalem, Israel