# nLab quantum operator (in geometric quantization)

for the moment the conent that would go here is rather at quantum observable

# Contents

## Idea

In the contect of geometric quantization a prequantum operator is a linear operator that presents an observable in quantum mechanics/quantum field theory once a polarization is chosen.

More in detail, the quantomorphism group $\mathbf{Aut}(\mathbf{c}_{conn})$ naturally acts on the space of sections $\mathbf{\Gamma}_X(E)$ of the prequantum line bundle.

$\widehat {(-)} : \mathbf{\Gamma}_X(E) \times \mathbf{Aut}(\mathbf{c}_{conn}) \to \mathbf{\Gamma}_X(E) \,.$

For $O \in \mathbf{Aut}(\mathbf{c}_{conn})$ a given Hamiltonian symplectomorphism with Hamiltonian, the corresponding map

$\widehat{O} : \mathbf{\Gamma}_X(E) \to \mathbf{\Gamma}_X(E)$

is the prequantum operator that quantizes $O$.

Revised on October 12, 2013 21:51:40 by Toby Bartels (98.19.41.253)