Gauge theories with nonunitary parallel transport [Elektronische Ressource] / vorgelegt von Thorsten Prüstel

Gauge Theorieswith Nonunitary ParallelTransportDissertationzur Erlangung des Doktorgradesdes Fachbereichs Physikder Universit at Hamburgvorgelegt vonThorsten Prustelaus BremerhavenHamburg 2003Gutachter der Doktorarbeit: Prof. Dr. G. MackProf. Dr. K. FredenhagenGutachter der Disputation: Prof. Dr. G. MackProf. Dr. J. LouisDatum der Disputation: 28.11.2003Vorsitzenderdes Pruf ungsausschusses: Dr. H.D. RuterVorsitzenderdes Promotionsausschusses: Prof. Dr. R. WiesendangerDekan des Fachbereichs Physik: Prof. Dr. G. HuberAbstractInallgaugetheories, includinggeneralrelativity, paralleltransportersareoffundamental importance. They are unitary maps between vector spaces atdierent space time points. It is proposed to abandon unitarity as a generalrequirement. The proposal is motivated by the fact that in discrete calculusand di erential geometry unitarity is not a natural requirement, and by adesire to interpret Higgs elds geometrically.The present thesis discusses gauge theories with nonunitary paralleltransport both in the continuum and on a graph.Vierbein elds can be identi ed as parts of nonunitary parallel trans-porters in the conventional four space time dimensions. Assuming invert-ibility of the parallel transporters it is shown how general relativity ts intothisframework. Metricityisobtainedautomaticallywithoutneedtoassumeit.