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dc.contributor.advisor Schick, Thomas Prof. Dr.
dc.contributor.author Lessel, Bernadette
dc.date.accessioned 2018-11-26T10:15:15Z
dc.date.available 2018-11-26T10:15:15Z
dc.date.issued 2018-11-26
dc.identifier.uri http://hdl.handle.net/11858/00-1735-0000-002E-E512-4
dc.language.iso eng de
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc 510 de
dc.title Shape space in terms of Wasserstein geometry and application to quantum physics de
dc.type doctoralThesis de
dc.contributor.referee Schick, Thomas Prof. Dr.
dc.date.examination 2018-06-28
dc.description.abstracteng This thesis offers a mathematical framework to treat quantum dynamics without reference to a background structure, but rather by means of the change of the shape of the state. For this, Wasserstein geometry is used. The so called Shape space, then, is defined as the quotient space of a Wasserstein space modulo the action of the isometry group of the background space. On Shape space we find a natural metric distance, the Shape distance, of which we investigate topological, metric and geodesic properties. Canonically mapped solutions of the Schrödinger equation turn out to be naturally nice curves in Shape space and some even constitue geodesics there. To also be able to speak about infinitesimal change of shapes, a definition for a tangent space at a point in Shape space is defined and applied. Finally a notion of differentiability for maps between Wasserstein spaces is proposed. de
dc.contributor.coReferee Bahns, Dorothea Prof. Dr.
dc.contributor.thirdReferee Sturm, Anja Prof. Dr.
dc.contributor.thirdReferee Witt, Ingo Prof. Dr.
dc.contributor.thirdReferee Jotz Lean, Madeleine Prof. Dr.
dc.contributor.thirdReferee Rehren, Karl-Henning Prof. Dr.
dc.subject.eng Wasserstein geometry de
dc.subject.eng Quantum physics de
dc.subject.eng Shape space de
dc.subject.eng Mathematical physics de
dc.subject.eng Quantum foundations de
dc.identifier.urn urn:nbn:de:gbv:7-11858/00-1735-0000-002E-E512-4-6
dc.affiliation.institute Fakultät für Mathematik und Informatik de
dc.subject.gokfull Mathematik (PPN61756535X) de
dc.identifier.ppn 1041060416

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