  In has been recently shown [1] that in Dirac's hole theory the vacuum state
is not the minimum energy state but that there exist quantum states with less
energy than that of the vacuum state. In this paper we extend this discussion
to quantum field theory (QFT) and consider the question of whether or not the
vacuum in QFT is the state of minimum energy. It will be shown that for a
"simple" field theory, consisting of a quantized fermion field interacting with
a classical electric field in 1-1D space-time, there exist quauntum states with
less energy than that of the vacuum state.
