# 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} }

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.

## 7 Citations

### Direct Images, Fields of Hilbert Spaces, and Geometric Quantization

- MathematicsCommunications in Mathematical Physics
- 2014

Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family Hs of Hilbert spaces, and the question arises if the spaces Hs are…

### Coherent states for compact Lie groups and their large-N limits

- Mathematics
- 2018

The first two parts of this article surveys results related to the heat-kernel coherent states for a compact Lie group K. I begin by reviewing the definition of the coherent states, their resolution…

### A unitary ‘quantization commutes with reduction’ map for the adjoint action of a compact Lie group

- MathematicsThe Quarterly Journal of Mathematics
- 2018

Let $K$ be a simply connected compact Lie group and $T^{\ast}(K)$ its cotangent bundle. We consider the problem of "quantization commutes with reduction" for the adjoint action of $K$ on…

### Direct Images, Fields of Hilbert Spaces, and Geometric Quantization

- Mathematics
- 2010

Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family Hs of Hilbert spaces, and the question arises if the spaces Hs are…

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