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Smooth structures on the field of prequantum Hilbert spaces

Volume 252 / 2020

Róbert Szőke 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.

Authors

  • Róbert SzőkeDepartment of Analysis, Institute of Mathematics
    ELTE Eötvös Loránd University
    Pázmány Péter sétány 1/c
    Budapest 1117, Hungary
    e-mail

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