Classical Foundations for a Quantum Theory of Time in a Two-Dimensional Spacetime
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 giv...
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| Format: | Others |
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DigitalCommons@USU
2010
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| Online Access: | https://digitalcommons.usu.edu/etd/708 https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=1704&context=etd |
| Summary: | 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. |
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