Term of Award
Master of Science in Mathematics (M.S.)
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Thesis (open access)
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This work is licensed under a Creative Commons Attribution 4.0 License.
Department of Mathematical Sciences
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In this thesis we classify all symplectic manifolds admitting a transitive, 2-form preserving action of the Galilei group G. Using the moment map and a theorem of Kirillov-Kostant-Souriau, we reduce the problem to that of classifying the coadjoint orbits of a central extension of G discovered by Bargmann. We then develop a systematic inductive technique to construct a cross section of the coadjoint action. The resulting symplectic orbits are interpreted as the manifolds of classical motions of elementary particles with or without spin, mass, and color.
Davis, Michael S., "Homogeneous Symplectic Manifolds of the Galilei Group" (2012). Electronic Theses and Dissertations. 866.
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