Quarks and gluons in the phase diagram of quantum chromodynamics
In this dissertation we study the phase diagram of strongly interacting matter by approaching the theory of quantum chromodynamics in the functional approach of Dyson Schwinger equations. With these quantum (field) equations of motions we calculate the non perturbative quark propagator within the Matsubara formalism. We built up on previous works and extend the so called truncation scheme, which is necessary to render the infinite tower of Dyson Schwinger equations finite and study phase transitions of chiral symmetry and the confinement/deconfinement transition. In the first part of this thesis we discuss general aspects of quantum chromodynamics and introduce the Dyson Schwinger equations in general and present the quark Dyson Schwinger equation together with its counterpart for the gluon. The BetheSalpeter equation is introduced which is necessary to perform two body bound state calculations. A view on the phase diagram of quantum chromodynamics is given, including the discussion of order parameter for chiral symmetry and confinement. Here we also discuss the dependence of the phase structure on the masses of the quarks. In the following we present the truncation and our results for an unquenched Nf 2 1 calculation and compare it to previous studies. We highlight some complementary details for the quark and gluon propagator and discus the resulting phase diagram, which is in agreement with previous work. Results for an equivalent of the Columbia plot and the critical surface are discussed. A systematically improved truncation, where the charm quark as a dynamical quark flavour is added, will be presented in Ch. 4. An important aspect in this investigation is the proper adjustment of the scales. This is done by matching vacuum properties of the relevant pseudoscalar mesons separately for Nf 2 1 and Nf 2 1 1 via a solution of the Bethe Salpeter equation. A comparison of the resulting Nf 2 1 and Nf 2 1 1 phase diagram indicates that a dynamical charm quark has no influence on the phase structure. An open question about the phase diagram of quantum chromodynamics is the importance of hadronic degrees of freedom. These are subject to an exploratory study