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dc.contributor.authorLeBlanc, Maurice Joseph
dc.date.accessioned2014-03-04T21:02:33Z
dc.date.available2014-03-04T21:02:33Z
dc.date.issued2013-05
dc.identifier.otherleblanc_maurice_j_201305_phd
dc.identifier.urihttp://purl.galileo.usg.edu/uga_etd/leblanc_maurice_j_201305_phd
dc.identifier.urihttp://hdl.handle.net/10724/28801
dc.description.abstractWhile much work toward constructing quantum field theories has already been done in the case of a flat space-time, the discipline is not nearly as well-developed in the case of a curved space-time. The axioms offered by Wightman provide a mathematically rigorous system for the construction of a quantum field theory on Minkowski space. I extend this axiomatic approach in order to develop a model for a free scalar quantum field theory in the case of a two-dimensional curved space-time by offering a set of axioms for a quantum state field which can then be used to create a quantum operator field by second quantization using the Segal field operator. I then demonstrate an example of a mathematically rigorous free scalar quantum field theory on a curved space-time satisfying these axioms. Finally I use Wigner's contraction method to demonstrate that these free quantum fields on the curved ax+b space-time limit to certain quantum fields on the flat plane, R^2.
dc.languageeng
dc.publisheruga
dc.rightspublic
dc.subjecthomogeneous two-dimensional curved space-time
dc.subjectquantum state field
dc.subjectfree scalar quantum field theory
dc.subjectWightman axioms
dc.subjectMackey machine
dc.titleAnalyzing free quantum field theories on the ax + b space-time and Wigner contractions to the Minkowski plane
dc.typeDissertation
dc.description.degreePhD
dc.description.departmentMathematics
dc.description.majorMathematics
dc.description.advisorRobert Varley
dc.description.committeeRobert Varley
dc.description.committeeShuzhou Wang
dc.description.committeeMichael Usher
dc.description.committeeEdward Azoff


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