Classical Foundations for a Quantum Theory of Time in a Two-Dimensional Spacetime

• Main Author: Carruth, Nathan Thomas
• Format: Others
• Published: DigitalCommons@USU 2010
• Subjects: Covers of diffeomorphism and infinite-dimensional topological groups; Diffeomorphism groups; Group-theoretic quantization; Infinite-dimensional topological groups; physics theory; theoretical mathematics; Mathematics; Physics
• Online Access: https://digitalcommons.usu.edu/etd/708; https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=1704&context=etd

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.