  We non-perturbatively study the fermion spectrum in the chiral symmetric
phase focusing on the effects of in-medium corrections for gauge boson. The
fermion spectrum is derived by solving the Schwinger-Dyson equation (SDE) with
ladder approximation on the real time axis. It is shown that the peak of the
fermion spectral function is broadened by in-medium effects for gauge boson
compared with the peak obtained with the tree gauge boson propagator. The peak
becomes much broader as the value of the gauge coupling increases. This
broadening is caused by multiple scatterings of fermions and gauge bosons
included through the non-perturbative resummation done by the SDE. In
particular, the Landau damping of gauge boson propagator plays an important
role in the broadening. Our results show no clear peak in the strong coupling
region, implying the disappearance of quasi-fermions in the strongly coupled
plasma. This indicates that quasi-particle picture may be no longer valid in
the strongly coupled QGP.
