Kinetics of QCD phase transitions in effective models

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Within the standard model of elementary particles the strong interaction is described by quantum chromodynamics (QCD), which is a non-Abelian gauge theory showing the fundamental properties of asymptotic freedom (i.e., the effective coupling becomes weak at collisions with large energy-momentum transfer) and confinement (i.e., the elementary constituents, the quark and gluons, cannot be observed as free particles but are bound in hadrons (mesons as bound states of a quark and an anti-quark and baryons as bound states of three quarks) that carry vanishing net-color charge.Thus, one expects that in a hot and dense medium of strongly interacting particles at some critical temperature and/or density the quarks and gluons can move quasi freely within that medium. This implies that a kind of phase transition occurs where the relevant degrees of freedom are not anymore hadrons but quarks and gluons ("partons"). This state of matter is called the quark-gluon plasma (QGP).In addition to the fundamental local color-gauge symmetry, in the light-quark sector (up, down, strange quarks) QCD is also characterized by an approximate chiral symmetry, which is spontaneously broken in the vacuum and at low temperatures and densities due to the formation of a quark condensate. At high temperatures one expects a "melting" of this quark condensate and thus the restoration of chiral symmetry.From lattice-QCD calculations in thermal equilibrium on knows that at high temperatures and low net-baryon densities the phase transitions are continuous "crossover transitions", while effective hadronic models suggest that at high temperatures and/or net-baryon densities the phase transition becomes of 1st order. This suggests further that this line of a first-order phase transition ends in a critical point, where the phase transition becomes of 2nd order.Now one hopes to find signatures of such first-order phase transitions or even a critical point in ultrarelativistic heavy-ion collisions. Possible signatures are fluctuations of conserved quantum numbers like the net-baryon number which are quantified by comulants of the corresponding statistical distributions. The main goal of our project is the quantum-field theoretical investigation whether such fluctuations can build up in a finite system of finite lifetime as the "fireballs" created in heavy-ion collisions. To that end we want to investigate effective quantum-field theoretical models (like the chiral quark-meson model) in nonequilibrium situations close to phase transitions and at the critical point, using the real-time formulation of relativistic many-body quantum-field theory (Schwinger-Keldysh formalism) both analytically (by deriving the appropriate Kadanoff-Baym equations and related semi-classical transport equations) and in computer simulations.