Smooth structures on the field of prequantum Hilbert spaces
Volume 252 / 2020
Studia Mathematica 252 (2020), 83-91
MSC: Primary 53D50; Secondary 32L10.
DOI: 10.4064/sm181211-16-3
Published online: 20 November 2019
Abstract
When there is a family of complex structures on the phase space, parametrized by a set $S$, the prequantum Hilbert spaces produced by geometric quantization, using the half-form correction, also depend on these parameters. This way we obtain a field of Hilbert spaces $p:H^{\mathop{\rm prQ}\nolimits }\rightarrow S$. We show that this field can have natural inequivalent smooth Hilbert bundle structures.
