Nonequilibrium pion dynamics near the critical point in a constituent quark model

Abstract We study static and dynamical critical phenomena of chiral symmetry breaking in a two-flavor Nambu–Jona-Lasinio constituent quark model. We obtain the low-energy effective action for scalar and pseudoscalar degrees of freedom to lowest order in quark loops and to quadratic order in the meson fluctuations around the mean field. The static limit of critical phenomena is shown to be described by a Ginzburg–Landau effective action including spatial gradients. Hence static critical phenomena is described by the universality class of the O(4) Heisenberg ferromagnet. Dynamical critical phenomena is studied by obtaining the equations of motion for pion fluctuations. We find that for T