We present a simple calculation of the nucleon self-energy in nuclear matter
at finite temperature in a relativistic framework, using the real time thermal
field theory. The imaginary parts of one-loop graphs are identified with
discontinuities across the unitary and the Landau cuts. We find that in general
both the cuts contribute significantly to the spectral function in the region
of (virtual) nucleon mass usually considered, even though the unitary cut is
ignored in the literature. Also our relativistic spectral function differs from
the one in non-relativistic approximation, used in some earlier calculations.