  We study Boltzmann-Fermi-Dirac equation when quantum effects are taken into
account in dilute gas dynamics. By employing new estimates on trilinear terms
of collision kernels, we prove the global existence of the classical solution
to Boltzmann-Fermi-Dirac equation near equilibrium. Furthermore, the limit from
Boltzmann-Fermi-Dirac equation to incompressible Navier-Stokes-Fourier
equations is justified rigorously. The corresponding formal analysis was given
in the thesis of Zakrevskiy \cite{Zakrevskiy}
