Abstract
These lectures review recent theoretical work suggesting that hadronic matter may dissolve into a weakly interacting quark-gluon plasma phase at energy densities only one order of magnitude above the ground state energy density of nuclei. Basic techniques of field theory used for calculating thermodynamic properties of Quantum Chromodynamics (QCD) are introduced. Functional methods are applied to develop QCD perturbation theory at finite temperatures and chemical potentials. The relevance of asymptotic freedom at high T, μ is motivated. We then confront the main skeleton in the QCD closet, namely, the nonperturbative color magnetic sector. Techniques of lattice gauge theories to get beyond the limitations of perturbation theory are then discussed. Recent numerical results are critically assessed.
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