Physics of Thermal QCD

We give a review of modern theoretical understanding of the physics of QCD at finite temperature. Three temperature regions are studied in details. When the temperature is low, the system presents a rarefied pion gas adequately described by chiral perturbation theory. When the temperature is increased, other than pion degrees of freedom are excited, the interaction between the particles in the heat bath becomes strong, and the chiral theory is not applicable anymore. At some point $T = T_c$ a phase transition is believed to occur The dynamics and the very existence of this phase transition strongly depends on the nature of the gauge group, the number of light quark flavors, and on the value of quark masses. If the quarks are very heavy, the order parameter associated with the phase transition is the correlator of Polyakov loops $_T$ related to the static potential between heavy colored sources. When the quark masses are small, the proper order parameter is the quark condensate $<\bar q q>_T$ and the phase transition is associated with the restoration of the chiral symmetry. Its dynamics is best understood in the framework of the instanton liquid model. Theoretical estimates and some numerical lattice measurements indicate that the phase transition probably does not occur for the experimentally observed values of quark masses. We have instead a very sharp crossover, "almost" a second order phase transition. At high temperatures $T \gg \mu_{hadr}$ the system is adequately described in terms of quark and gluon degrees of freedom and presents the quark-gluon plasma (QGP). Static and kinetic properties of QGP are discussed. A particular attention is payed to the problem of physical observability.