Nickel, Marcel Dominik Johannes
Color-superconductivity from a Dyson-Schwinger perspective.
Technische Universität, Darmstadt
[Ph.D. Thesis], (2007)
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|Item Type:||Ph.D. Thesis|
|Title:||Color-superconductivity from a Dyson-Schwinger perspective|
Color-superconducting phases of quantum chromodynamics at vanishing temperatures and high densities are investigated. The central object is the one-particle Green's function of the fermions, the so-called quark propagator. It is determined by its equation of motion, the Dyson-Schwinger equation. To handle Dyson-Schwinger equations a successfully applied truncation scheme in the vacuum is extended to finite densities and gradually improved. It is thereby guaranteed that analytical results at asymptotically large densities are reproduced. This way an approach that is capable to describe known results in the vacuum as well as at high densities is applied to densities of astrophysical relevance for the first time. In the first part of the thesis the framework of the investigations with focus on the extension to finite densities is outlined. Physical observables are introduced which can be extracted from the propagator. In the following a minimal truncation scheme is presented. To point out the complexity of our approach in comparison to phenomenological models of quantum chromodynamics the chirally unbroken phase is discussed first. Subsequently color-superconducting phases for massless quarks are investigated. Furthermore the role of finite quark masses and neutrality constraints at moderate densities is studied. In contrast to phenomenological models the so-called CFL phase is found to be the ground state for all relevant densities. In the following part the applicability of the maximum entropy method for the extraction of spectral functions from numerical results in Euclidean space-time is demonstrated. As an example the spectral functions of quarks in the chirally unbroken and color-superconducting phases are determined. Hereby the results of our approach are presented in a new light. For instance the finite width of the quasiparticles in the color-superconducting phase becomes apparent. In the final chapter of this work extensions of our truncation scheme in particular the back-reaction of so-called Goldstone bosons are elaborated. As those extensions in our framework have not been carried out for the vacuum either, the modification of the quark propagator in the chirally broken vacuum is initially discussed. Hereafter this approach is enlarged to the CFL phase for the case of vanishing quark masses. Simultaneously low-energy properties of Goldstone bosons are studied. Finally a self-consistent truncation for the modification of the interaction is worked out, which implements the Meissner effect.
|Place of Publication:||Darmstadt|
|Classification DDC:||000 Allgemeines, Informatik, Informationswissenschaft > 000 Allgemeines, Wissenschaft|
|Divisions:||05 Department of Physics|
|Date Deposited:||17 Oct 2008 09:22|
|Last Modified:||07 Dec 2012 11:53|
|Referees:||Wambach, Prof.Dr. Jochen and Berges, Prof.Dr. Jürgen|
|Advisors:||Wambach, Prof.Dr. Jochen|
|Refereed:||11 June 2007|