The low-energy effective theory of QCD at small quark masses in a finite volume [Elektronische Ressource] / vorgelegt von Christoph Lehner

The low-energy effective theory ofQCD at small quark masses in afinite volumeD I S S E R T A T I O Nzur Erlangung des Doktorgradesder Naturwissenschaften (Dr. rer. nat.)der Naturwissenschaftlichen Fakultat¨ II - Physikder Universitat¨ Regensburgvorgelegt vonChristoph Lehneraus RegensburgJanuar 2010Promotionsgesuch eingereicht am: 30.11.2009Die Arbeit wurde angeleitet von: Prof. Dr. Tilo Wettig¨PRUFUNGSAUSSCHUSS:Vorsitzender: Prof. Dr. Christian Back1. Gutachter: Prof. Dr. Tilo Wettig2. Prof. Dr. Andreas Schafer¨weiterer Prufer:¨ Prof. Dr. Jaroslav FabianAbstractAt low energies the theory of quantum chromodynamics (QCD) can be described effectively in termsof the lightest particles of the theory, the pions. This approximation is valid for temperatures wellbelow the mass difference of the pions to the next heavier particles.We study the low-energy effective theory at very small quark masses in a finite volumeV . Thepcorresponding perturbative expansion in 1= V is called" expansion. At each order of this expansiona finite number of low-energy constants completely determine the effective theory. These low-energyconstants are of great phenomenological importance.In the leading order of the" expansion, called" regime, the theory becomes zero-dimensional andis therefore described by random matrix theory (RMT).