  Using the Zubarev quantum-statistical density operator, we calculated the
corrections to the energy-momentum tensor of a massless fermion gas associated
with acceleration. It is shown that when fourth-order corrections are taken
into account, the energy-momentum tensor in the laboratory frame is equal to
zero at a proper temperature measured by a comoving observer equal to Unruh
temperature. Consequently, the Minkowski vacuum is visible to the accelerated
observer as a medium filled with a heat bath of particles with the Unruh
temperature, which is the essence of the Unruh effect.
