  It is well known that there can be negative energy densities in quantum field
theory. Most of the work done in this area has involved free non-interacting
systems. In this paper we show how a quantum state with negative energy density
can be formulated for a Dirac field interacting with an Electromagnetic field.
It will be shown that, for this case, there exist quantum states whose average
energy density over an arbitrary volume is a negative number with an
arbitrarily large magnitude.
