Uniqueness in geometric quantization

Laszlo Lempert (Purdue)

Geometric quantization often produces not one Hilbert space to represent the quantum states of a physical system but a whole family H_s of Hilbert spaces, and the question arises if the spaces H_s are canonically isomorphic. In the early 1990s Hitchin and Axelrod-Della Pietra-Witten suggested to view H_s as fibers of a Hilbert bundle H, introduce a connection on H and use parallel transport to identify different fibers. In the talk I will discuss to what extent this can be done.