Smooth structures on the field of prequantum Hilbert spaces
Mathematical Physics
2018-08-14 v1 Differential Geometry
Functional Analysis
math.MP
Abstract
When there is a family of complex structures on the phase space, parametrized by a set , the prequantum Hilbert spaces produced by geometric quantization, using the half-form correction, also depends on these parameters. This way we obtain a field of Hilbert spaces . We show that this field can have natural inequivalent smooth Hilbert bundle structures.
Cite
@article{arxiv.1808.03918,
title = {Smooth structures on the field of prequantum Hilbert spaces},
author = {Róbert Szőke},
journal= {arXiv preprint arXiv:1808.03918},
year = {2018}
}