Dressed Quark Propagator at Finite Temperature in the Schwinger-Dyson approach with the Rainbow Approximation - exact numerical solutions and their physical implication

The Schwinger-Dyson equation for the quark in the rainbow approximation at finite temperature (T) is solved numerically without introducing any ansatz for the dressed quark propagator. The dymanical quark mass-function and the wave-function renormalization are found to have non-trivial dependence on three-momentum, Matsubara-frequency and temperature. The critical temperature of the chiral phase transition (T_c) and the T-dependence of the quark condensate are highly affected by the wave-function renormalization. We found that T_c \simeq 155 MeV which is consistent with the result of the finite temperature lattice QCD simulation. It is also found that the system is not a gas of free quarks but a highly interacting system of quarks and gluons even in the chirally symmetric phase.