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Smooth structures on the field of prequantum Hilbert spaces (1808.03918v1)
Published 12 Aug 2018 in math-ph, math.DG, math.FA, and math.MP
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 depends on these parameters. This way we obtain a field of Hilbert spaces $p:H{pr Q}\rightarrow S$. We show that this field can have natural inequivalent smooth Hilbert bundle structures.
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