Classical and quantum gravity with Ashtekar variables

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dc.contributor.authorSoo, Chopinen
dc.contributor.committeechairChang, Lay Namen
dc.contributor.committeememberBlecher, Marvinen
dc.contributor.committeememberDennison, Brian K.en
dc.contributor.committeememberMarshak, Robert E.en
dc.contributor.committeememberZia, Royce K. P.en
dc.contributor.departmentPhysicsen
dc.date.accessioned2014-03-14T21:15:05Zen
dc.date.adate2006-06-19en
dc.date.available2014-03-14T21:15:05Zen
dc.date.issued1992en
dc.date.rdate2006-06-19en
dc.date.sdate2006-06-19en
dc.description.abstractThis thesis is a study of classical and quantum gravity with Ashtekar variables. The Ashtekar constraints are shown to capture the essence of the constraints and constraint algebra of General Relativity in four dimensions. A classification scheme of the solution space of the Ashtekar constraints is proposed and the corresponding physics is investigated. The manifestly covariant equations of motion for the Ashtekar variables are derived. Explicit examples are discussed and new classical solutions of General Relativity are constructed by exploiting the properties of the Ashtekar variables. Non-perturbative canonical quantization of the theory is performed. The ordering of the quantum constraints as well as the formal closure of the quantum constraint algebra are explored. A detailed Becchi-Rouet-Stora-Tyutin (BRST) analysis of the theory is given. The results demonstrate explicitly that in quantum gravity, fluctuations in topology can occur and there are strong evidences of phases in the theory. There is a phase which is described by a topological quantum field theory (TQFT) of the Donaldson-Witten type and an Abelian antiinstanton phase wherein self-interactions of the gravitational fields produce symmetry breaking from SO(3) to U(1). The full theory is much richer and includes fluctuations which bring the system out of the various restricted sectors while preserving diffeomorphism invariance. Invariants of the quantum theory with are constructed through BRST descents. They provide a clear and systematic characterization of non-local observables in quantum gravity, and can yield further differential invariants of four-manifolds.en
dc.description.degreePh. D.en
dc.format.extentvii, 102 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-06192006-125720en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06192006-125720/en
dc.identifier.urihttp://hdl.handle.net/10919/38626en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1992.S671.pdfen
dc.relation.isformatofOCLC# 27379287en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1992.S671en
dc.subject.lcshGravityen
dc.subject.lcshQuantum gravityen
dc.titleClassical and quantum gravity with Ashtekar variablesen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplinePhysicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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