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- http://jmp.aip.org/resource/1/jmapaq/v49/i3/p032104_s1
- http://link.aip.org/link/?JMAPAQ/49/032104/1
- http://arxiv.org/abs/0708.1539

Journal | Journal of Mathematical Physics |
---|---|

Date | Published - 7 Mar 2008 |

Issue number | 3 |

Volume | 49 |

Number of pages | 22 |

Pages (from-to) | 1-22 |

Original language | English |

On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called Misra–Bugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hidden-variable model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed.

© 2008 American Institute of Physics. This is an author produced version of a paper published in Journal of Mathematical Physics. Uploaded in accordance with the publisher's self-archiving policy.

- quantum probability, statistical model, hidden variables, projective Hilbert space

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