Phase transitions in strongly interacting quantum field theories: QED_3 vs. QCD

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BonnetJacqueline_2013_10_16.pdf (1.74 MB)

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2013

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DOI:
http://dx.doi.org/10.22029/jlupub-9610

Abstract

In this thesis, we investigate strongly coupled quantum field theories on the examples of (2+1) dimensional Quantumelectrodynamics (QED_3) and (3+1) dimensional Quantum Chromodynamics (QCD) in the framework of Dyson-Schwinger equations. We firstly focus on the chiral phase transition in QED_3 as a low-energy effective theory for high-temperature superconductors. These materials are inherently anisotropic, as shown by experiments. We therefore focus on the influence of an anisotropic spacetime onto the critical number of fermion flavors for chiral symmetry breaking at zero and finite temperature. The findings are summarized in phase diagrams for the critical number of fermion flavors as a function of the independent anisotropic velocities and temperature. These were the first calculations considering anisotropic QED_3 at finite temperatures. Furthermore, the presented investigations elaborate on the critical scaling behavior close to the merging region of the thermal phase transition line and the quantum phase transition point. The most important results include the finding that anisotropy provides an external parameter that determines the scaling scenario. Secondly, the QCD part of this thesis consists of a feasibility study of the implementation of external magnetic fields into the Dyson-Schwinger formalism. This study serves as a basis for further investigations of e.g. the dynamical mass generation at finite temperatures and densities. This will allow to contribute to the discussions on the phenomenon of (inverse) magnetic catalysis from a functional methodsĀ“ point of view. Furthermore, we present the first successful extraction of a dressed Wilson loop from Dyson- Schwinger equations. It represents an observable for confinement that was recently introduced in the framework of lattice gauge theory. In addition, its connection with the conventional Wilson loop allows for a direct extraction of the string tension.

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