Homogeneous Symplectic Manifolds of the Galilei Group

<p>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.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2012

Author dc:creator

• Davis, Michael S.

Contributors dc:contributor

• Xiezhang Li
• Scott Kersey
• Yi Lin

• ETD
• Symplectic manifold
• Coadjoint orbit
• Differential 2-form
• Galilei group
• Mathematics

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/866

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-1875