Effective Polyakov Loop Modeling of QCD - A Field Theoretical Study of the Phase Diagram of Quark Matter

In this thesis we study the phase diagram of two-flavor quantum chromodynamics with effective models. We investigate the phase diagram in the baryon chemical potential temperature and magnetic field temperature planes. As approximations to QCD we use the Polyakov-loop extended quark-meson model and the Pisarski- Skokov chiral matrix model. We take quantum and thermal fluctuations of quarks into account to one loop, while we neglect bosonic fluctuations. Bosonic self-energy cor- rections are calculated in order to consistently fix coupling constants at the one-loop level in the large-Nc limit.