Date of Award:
Master of Science (MS)
Charles G. Torre
We consider the set of all spacelike embeddings of the circle S1 into a spacetime R1 × S1 with a metric globally conformal to the Minkowski metric. We identify this set and the group of conformal isometries of this spacetime as quotients of semidirect products involving diffeomorphism groups and give a transitive action of the conformal group on the set of spacelike embeddings. We provide results showing that the group of conformal isometries is a topological group and that its action on the set of spacelike embeddings is continuous. Finally, we point out some directions for future research.
Carruth, Nathan Thomas, "Classical Foundations for a Quantum Theory of Time in a Two-Dimensional Spacetime" (2010). All Graduate Theses and Dissertations. 708.
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