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Title: Quantum models of space-time based on recoupling theory
Author: Moussouris, John Peter
ISNI:       0000 0001 3428 1347
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 1984
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Models of geometry that are intrinsically quantum-mechanical in nature arise from the recoupling theory of space-time symmetry groups. Roger Penrose constructed such a model from SU(2) recoupling in his theory of spin networks; he showed that spin measurements in a classical limit are necessarily consistent with a three-dimensional Euclidian vector space. T. Regge and G. Ponzano expressed the semi-classical limit of this spin model in a form resembling a path integral of the Einstein-Hilbert action in three Euclidian dimensions. This thesis gives new proofs of the Penrose spin geometry theorem and of the Regge-Ponzano decomposition theorem. We then consider how to generalize these two approaches to other groups that give rise to new models of quantum geometries. In particular, we show how to construct quantum models of four-dimensional relativistic space-time from the re-coupling theory of the Poincare group.
Supervisor: Penrose, Roger Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Combinatorics ; Geometry ; Group theory and generalizations (mathematics) ; Mechanics of particles and systems (mathematics) ; Quantum theory (mathematics) ; Theoretical physics ; quantum ; relativity ; groups ; recoupling ; spin networks ; penrose ; racah ; regge ; ponzano ; poincare group