The quark propagator is calculated in the Nambu–Jona-Lasinio model in a self-consistent $1/N_c$-expansion at next-to-leading order. The calculations are carried out iteratively in Euclidean space. The chiral quark condensate and its dependence on temperature and chemical potential is calculated directly and compared with the mean-field results. In the chiral limit, we find a second-order phase transition at finite temperature and zero chemical potential, in agreement with universality arguments. At zero temperature and finite chemical potential, the phase transition is first order. In comparison with the mean-field results, the critical temperature and chemical potential are slightly reduced. We determine spectral functions from the Euclidean propagators by employing the maximum-entropy method. Thereby quark and meson masses are estimated and decay channels identified. For testing this method, we also apply it to evaluate perturbative spectral functions, which can be calculated directly in Minkowski space. In most cases we find that the maximum-entropy method is able to reproduce the rough features of the spectral functions, but not the details.

• Received 8 March 2010

DOI:https://doi.org/10.1103/PhysRevD.81.094022