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dc.contributor.authorReginatto, Marcelen_US
dc.contributor.authorHall, Michaelen_US
dc.date.accessioned2017-04-24T13:44:36Z
dc.date.available2017-04-24T13:44:36Z
dc.date.issued2012en_US
dc.date.modified2013-06-02T23:54:40Z
dc.identifier.issn0094-243Xen_US
dc.identifier.doi10.1063/1.3703625en_US
dc.identifier.urihttp://hdl.handle.net/10072/47063
dc.description.abstractWe consider the space of probabilities {P(x)}, where the x are coordinates of a config- uration space. Under the action of the translation group, P(x)?P(x+? ), there is a natural metric over the parameters ? given by the Fisher-Rao metric. This metric induces a metric over the space of probabilities. Our next step is to set the probabilities in motion. To do this, we introduce a canon- ically conjugate field S and a symplectic structure; this gives us Hamiltonian equations of motion. We show that it is possible to extend the metric structure to the full space of the (P;S), and this leads in a natural way to introducing a K䨬er structure; i.e., a geometry that includes compatible symplectic, metric and complex structures. The simplest geometry that describes these spaces of evolving probabilities has remarkable properties: the natural, canonical variables are precisely the wave functions of quantum mechanics; the Hamiltonian for the quantum free particle can be derived from a representation of the Galilean group using purely geometrical arguments; and it is straightforward to associate with this geometry a Hilbert space which turns out to be the Hilbert space of quantum mechanics. We are led in this way to a reconstruction of quantum theory based solely on the geometry of probabilities in motion.en_US
dc.description.peerreviewedYesen_US
dc.description.publicationstatusYesen_US
dc.format.extent119038 bytes
dc.format.mimetypeapplication/pdf
dc.languageEnglishen_US
dc.language.isoen_US
dc.publisherAmerican Institute of Physicsen_US
dc.publisher.placeUnited Statesen_US
dc.relation.ispartofstudentpublicationNen_US
dc.relation.ispartofpagefrom96en_US
dc.relation.ispartofpageto103en_US
dc.relation.ispartofjournalAIP Conference Proceedingsen_US
dc.relation.ispartofvolume1443en_US
dc.rights.retentionYen_US
dc.subject.fieldofresearchQuantum Physics not elsewhere classifieden_US
dc.subject.fieldofresearchcode020699en_US
dc.titleQuantum theory from the geometry of evolving probabilitiesen_US
dc.typeJournal articleen_US
dc.type.descriptionC1 - Peer Reviewed (HERDC)en_US
dc.type.codeC - Journal Articlesen_US
gro.rights.copyrightCopyright 2012 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in AIP Conference Proceedings, Vol. 1443, pp. 96-103 and may be found at dx.doi.org/10.1063/1.3703625.en_US
gro.date.issued2012
gro.hasfulltextFull Text


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