Non-Equilibrium Aspects of Chiral Field Theories

Abstract

First, the chiral phase transition at nonzero temperature and baryon chemical potential is studied at mean field level in the sigma model that includes quark degrees of freedom explicitly. For small bare quark masses the critical point separating the first order phase transition line and the smooth crossover region is determined, and the spinodal lines are drawn. Adiabatic lines are computed showing that the critical point does not serve as focusing point in the adiabatic expansion. Second, coarse-grained evolution equations for inhomogeneous chiral condensate fields coupled to a heat bath are derived in the linear sigma model. Multiple effects of the thermal background on the Disoriented Chiral Condensate (DCC) are studied within linear response theory. In-medium modification of the pion dispersion relation is examined. The deviation from the speed of light of the velocity of soft Goldstone modes is calculated. Decay widths of pions and sigma mesons are computed at nonzero temperature at one- and two-loop order in perturbation theory. We show that elastic scattering processes are significant for the dissipation of DCCs in the phase transition region. Throughout this work we made sure that Goldstone's Theorem is fulfilled when chiral symmetry is spontaneously broken.