Reformulation of the Hermitean 1-matrix model as an effective field theory [Elektronische Ressource] / vorgelegt von Alexander Klitz

Reformulation of theHermitean 1-Matrix Model asan Effective Field TheoryDissertationzurErlangung des Doktorgrades (Dr. rer. nat.)derMathematisch-Naturwissenschaftlichen FakultätderRheinischen Friedrich-Wilhelms-Universität Bonnvorgelegt vonAlexander KlitzausLünenBonn 2009Diese Dissertation ist auf dem Hochschulschriftenserver der ULB Bonn unterhttp://hss.ulb.uni-bonn.de/diss online elektronisch publiziert.Erscheinungsjahr: 2009AngefertigtmitGenehmigungderMathematisch-NaturwissenschaftlichenFakultätder Rheinischen Friedrich-Wilhelms-Universität BonnReferent: Prof. Dr. Rainald FlumeKorreferent: Prof. Dr. Albrecht KlemmTag der Promotion: 20. Juli 2009AbstractThe formal Hermitean 1-matrix model is shown to be equivalent to aneffective field theory. The correlation functions and the free energy of thematrix model correspond directly to the correlation functions and the freeenergy of the effective field theory. The loop equation of the field theorycoupling constants is stated. Despite its length, this loop equation issimpler than the loop equations in the matrix model formalism itself sinceit does not contain operator inversions in any sense, but consists insteadonly of derivative operators and simple projection operators. Therefore thesolution of the loop equation could be given for an arbitrary number of cutsup to the fifth order in the topological expansion explicitly.