Yang-Mills theory at finite temperatures

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The goal of the proposed research project is a detailed understanding of the phase diagram of QCD, in particular in the regime of finite baryon density which is currently unaccessible to lattice simulations. For this purpose the variational approaches to continuum quantum field theory at finite temperatures which were developed in the first funding period are supposed to be extended to full QCD at finite chemical potential. These variational approaches are based on either the Hamiltonian formulation of QCD in Coulomb gauge, or the covariant path integral approach in Landau gauge. In this context, it is planned to first study the relevant propagators at finite temperature and chemical potential, from which the order parameters for confinement (Polyakov loop) and chiral symmetry breaking (quark condensate), as well as the dual quark condensate will be computed. Furthermore, it is planned to study QCD at finite temperature and chemical potential in the presence of an external homogeneous magnetic field using the covariant variational approach. To this end, the technique of (approximate) partial summation of Landau levels developed in the first funding period shall be used to compute the quark condensate as a function of the magnetic field strength in the regime most relevant for relativistic heavy ion reactions. In addition to these continuum approaches, the quark propagators and vertices of relevance for the Hamiltonian approach in Coulomb gauge shall be studied by means of lattice simulations.