Show simple item record

Shape space in terms of Wasserstein geometry and application to quantum physics

dc.contributor.advisorSchick, Thomas Prof. Dr.
dc.contributor.authorLessel, Bernadette
dc.titleShape space in terms of Wasserstein geometry and application to quantum physicsde
dc.contributor.refereeSchick, Thomas Prof. Dr.
dc.description.abstractengThis 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
dc.contributor.coRefereeBahns, Dorothea Prof. Dr.
dc.contributor.thirdRefereeSturm, Anja Prof. Dr.
dc.contributor.thirdRefereeWitt, Ingo Prof. Dr.
dc.contributor.thirdRefereeJotz Lean, Madeleine Prof. Dr.
dc.contributor.thirdRefereeRehren, Karl-Henning Prof. Dr.
dc.subject.engWasserstein geometryde
dc.subject.engQuantum physicsde
dc.subject.engShape spacede
dc.subject.engMathematical physicsde
dc.subject.engQuantum foundationsde
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematik (PPN61756535X)de

Files in this item


This item appears in the following Collection(s)

Show simple item record