Term of Award
Fall 2012
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Francois Ziegler
Committee Member 1
Xiezhang Li
Committee Member 2
Scott Kersey
Committee Member 3
Yi Lin
Committee Member 3 Email
yilin@georgiasouthern.edu
Abstract
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.
Recommended Citation
Davis, Michael S., "Homogeneous Symplectic Manifolds of the Galilei Group" (2012). Electronic Theses and Dissertations. 866.
https://digitalcommons.georgiasouthern.edu/etd/866
Research Data and Supplementary Material
No
