Nonperturbative studies of quantum field theories on noncommutative spaces [Elektronische Ressource] / von Jan Volkholz

Nonperturbative Studies of Quantum FieldTheories on Noncommutative SpacesDISSERTATIONzur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. rer. nat.)im Fach Physikeingereicht an derMathematisch-Naturwissenschaftlichen Fakultät IHumboldt-Universität zu BerlinvonHerr Dipl.-Phys. Jan Volkholzgeboren in Schwerin/Meckl.Präsident der Humboldt-Universität zu Berlin:Prof. Dr. Dr. h.c. Christoph MarkschiesDekan der Mathematisch-Naturwissenschaftlichen Fakultät I:Prof. Dr. Christian LimbergGutachter:1. Prof. Dr. M. Müller-Preußker2. Prof. Dr. D. O’Connor3. Dr. H. Dorneingereicht am: 26. März 2007Tag der mündlichen Prüfung: 16. November 2007AbstractThis work deals with three quantum field theories on spaces with noncom-muting position operators. Noncommutative models occur in the study ofstring theories and quantum gravity. They usually elude treatment beyondthe perturbative level. Due to the technique of dimensional reduction, how-ever, we are able to investigate these theories nonperturbatively. This entailstranslating the action functionals into a matrix language, which is suitablefor numerical simulations.4First we explore the λφ model on a noncommutative plane. We inves-tigate the continuum limit at fixed noncommutativity, which is known asthe double scaling limit. Here we focus especially on the fate of the striped4phase, a phase peculiar to the noncommutative version of the regularizedλφmodel.