Effective Field Theories for Hot and Dense Matter
University of Wrocław, 50-204
2 Bogoliubov Laboratory for Theoretical Physics, JINR Dubna, 141980 Dubna, Russia
The lecture is divided in two parts. The ﬁrst one deals with an introduction to the physics of hot, dense many-particle systems in quantum ﬁeld theory [1, 2]. The basics of the path integral approach to the partition function are explained for the example of chiral quark models. The QCD phase diagram is discussed in the meanﬁeld approximation while QCD bound states in the medium are treated in the rainbow-ladder approximation (Gaussian ﬂuctuations). Special emphasis is devoted to the discussion of the Mott eﬀect, i.e. the transition of bound states to unbound, but resonant scattering states in the continnum under the inﬂuence of compression and heating of the system. Three examples are given: (1) the QCD model phase diagram with chiral symmetry ¨ restoration and color superconductivity , (2) the Schrodinger equation for heavy-quarkonia , and (2) Pions  as well as Kaons and D-mesons in the ﬁnite-temperature Bethe-Salpeter equation . We discuss recent applications of this quantum ﬁeld theoretical approach to hot and dense quark matter for a description of anomalous J/ψ supression in heavy-ion collisions  and for the structure and cooling of compact stars with quark matter interiors .
The second part provides a detailed introduction to the Polyakov-loop Nambu–Jona-Lasinio model  for thermodynamics and mesonic correlations  in the phase diagram of quark matter. Important relationships of low-energy QCD like the Gell-Mann–Oakes–Renner relation are generalized to ﬁnite temperatures. The eﬀect of including the coupling to the Polyakov-loop potential on the phase diagram and mesonic correlations is discussed. An outlook is given to eﬀects of nonlocality of the interactions  and of mesonic correlations in the medium  which go beyond the meanﬁeld description.
© Owned by the authors, published by EDP Sciences, 2010