Effective Field Theories for Hot and Dense Matter

¹ University of Wrocław, 50-204 Wrocław, Poland
² Bogoliubov Laboratory for Theoretical Physics, JINR Dubna, 141980 Dubna, Russia

Abstract

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 [3], (2) the Schrodinger equation for heavy-quarkonia [4], and (2) Pions [5] as well as Kaons and D-mesons in the finite-temperature Bethe-Salpeter equation [6]. 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 [7] and for the structure and cooling of compact stars with quark matter interiors [8].

The second part provides a detailed introduction to the Polyakov-loop Nambu–Jona-Lasinio model [9] for thermodynamics and mesonic correlations [10] 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 [11] and of mesonic correlations in the medium [12] which go beyond the meanfield description.