Curvature of fields of quantum Hilbert spaces

Physics – Mathematical Physics

Scientific paper

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Scientific paper

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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