This paper investigates the quantum Dirac field in n ＋ 1-dimensional flat spacetime and derives a lower bound in the form of quantum inequality on the energy density averaged against spacetime sampling functions. The stateindependent quantum inequality derived in the present paper is similar to the temporal quantum energy inequality and it is stronger for massive field than for massless one. It also presents the concrete results of the quantum inequality in 2 and 4-dimensional spacetimes.
