  Quantum Weak Energy Inequalities (QWEIs) have been established for a variety
of quantum field theories in both flat and curved spacetimes. Dirac fields are
known (by a result of Fewster and Verch) to satisfy QWEIs under very general
circumstances. However this result does not provide an explicit formula for the
QWEI bound, so its magnitude has not previously been determined. In this paper
we present a new and explicit QWEI bound for Dirac fields of arbitrary mass in
four-dimensional Minkowski space. We follow the methods employed by Fewster and
Eveson for the scalar field, modified to take account of anticommutation
relations. A key ingredient is an identity for Fourier transforms established
by Fewster and Verch. We also compare our QWEI with those previously obtained
for scalar and spin-1 fields.
