  In the real-time thermal field theory, the nucleon self-energy at finite
temperature and density is evaluated where an extensive set of pion-baryon
($\pi B$) loops are considered. On the other side the in-medium self-energy of
$N^*(1535)$ for $\pi N$ and $\eta N$ loops is also determined in the same
framework. The detail branch cut structures for these different $\pi B$ loops
for nucleon $N(940)$ and $\pi N$, $\eta N$ loops for $N^*(1535)$ are addressed.
Using the total self-energy of $N(940)$ and $N^*(1535)$, which contain the
contributions of their corresponding loop diagrams, the complete structures of
their in-medium spectral functions have been obtained. The Landau and unitary
cut contributions provide two separate peak structures in the nucleon spectral
function while $N^*(1535)$ has single peak structure in its unitary cuts. At
high temperature, the peak structures of both at their individual poles are
attenuated while at high density Landau peak structure of nucleon is completely
suppressed and its unitary peak structure is tending to be shifted towards the
melted peak of $N^*(1535)$. The non-trivial modifications of these chiral
partners may indicate some association of chiral symmetry restoration.
