# Curvature of fields of quantum Hilbert spaces

@article{Lempert2012CurvatureOF,
title={Curvature of fields of quantum Hilbert spaces},
author={L{\'a}szl{\'o} Lempert and R'obert SzHoke},
journal={arXiv: Mathematical Physics},
year={2012}
}
• Published 4 April 2012
• Mathematics
• arXiv: Mathematical Physics
We show that using the family of adapted K\"ahler polarizations of the phase space of a compact, simply connected, Riemannian symmetric space of rank-1, the obtained field $H^{corr}$ of quantum Hilbert spaces produced by geometric quantization including the half-form correction is flat if $M$ is the 3-dimensional sphere and not even projectively flat otherwise.
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