Short range correlations in quark and nuclear matter [Elektronische Ressource] / vorgelegt von Frank Frömel

Short-range correlationsin quark and nuclear matterDissertation zur Erlangung des Doktorgradesder Naturwissenschaftlichen Fakult¨ atder Justus-Liebig-Universit¨ at GießenFachbereich 07 – Mathematik und Informatik,Physik, Geographievorgelegt vonFrank Fr¨omelaus AltenstadtGießen, Juni 2007Dekan: Prof. Dr. Bernd BaumannI. Gutachter: Prof. Dr. Ulrich MoselII. Gutachter: PD Dr. Stefan LeupoldTag der mundlic¨ hen Prufung:¨ 18.07.2007Contents1 Introduction 12 The formalism 112.1 TheNJLinteraction........................... 12.2 1/N expansionintheNJLmodel......... 14c2.2.1 Order counting in 1/N ........... 14c2.2.2 Clasificationofself-energydiagrams... 152.2.3 TheRandomPhaseApproximation............... 172.3 Mean-fieldapproaches............... 182.3.1 TheO(1)Hartre+RPAapproach..... 182.3.2 Hartre–Fock,RPA,andGoldstonemodes........... 212.4 TheO(1/N)approach............... 24c2.4.1 CoupledsetofDyson–Schwingerequations... 242.4.2 Regularizationscheme........... 252.4.3 Furtherremarks............... 262.5 1/N corectionsandchiralsymmetry.................. 27c2.5.1 Chirally invariant 1/N extensions..... 28c2.5.2 Consequences for theO(1/N)approach............ 29c2.6 Quark fields and propagators ........... 322.6.1 Green’sfunctionsonaclosedtime-path............. 332.6.2 Lorentzstructure......................... 342.6.3 Quarkspectralfunction .......... 362.6.4 Real and imaginary parts of the propagators .......... 372.6.