English

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 SS, 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 p:HprQSp:H^{pr Q}\rightarrow S. We show that this field can have natural inequivalent smooth Hilbert bundle structures.

Keywords

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}
}
R2 v1 2026-06-23T03:31:11.853Z