Field theory on a non-commutative plane [Elektronische Ressource] / von Frank Hofheinz

Field Theory on a Non–Commutative PlaneA non–perturbative study of 2d gauge theory and 3d scalar theorybased on dimensional reductionD I S S E R T A T I O Nzur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. rer. nat.)im Fach Physikeingereicht an derMathematisch–Naturwissenschaftlichen Fakulta¨t IHumboldt–Universita¨t zu BerlinvonHerr Dipl.–Phys. Frank Hofheinzgeboren am 25.06.1966 in Neuenstadt a.K.Pr¨asident der Humboldt-Universita¨t zu Berlin:Prof. Dr. Ju¨rgen MlynekDekan der Mathematisch–Naturwissenschaftlichen Fakulta¨t I:Prof. Dr. Michael LinscheidGutachter:1. Prof. Dr. M. Muller–Preußker¨2. Prof. Dr. D. Lu¨st3. Prof. Dr. J. Ambjørneingereicht am: 10. Ma¨rz 2003Tag der mu¨ndlichen Pru¨fung: 30. Juni 2003AbstractIn the recent years there is a surge of interest in quantum field theories on spaceswith non–commutative coordinates. The potential applications of such models in-cludestringtheory,particlephenomenologyaswellassolidstatephysics.Weperforma non–perturbative study of such non–commutative field theories by the means ofMonte Carlo simulations. In particular we consider a two dimensional pure U(1)gauge field theory and a three dimensional scalar field theory. To this end we mapthe corresponding lattice theories on dimensionally reduced models, which are for-mulated in terms of N×N matrices.The 2d gauge theory on the lattice is equivalent to the twisted Eguchi–Kawaimodel, which we simulated atN ranging from 25 to 515.