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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.
It has been shown that there exist quantum states with less energy than the vacuum state for QED in the temporal gauge. In fact there is no lower bound to the energy of quantum states. If an initial state interacts with properly applied classical fields then it is possible to extract an arbitrarily large amount of energy from the initial state. The classical fields that were applied in this article are mathematical objects that are not assumed to correspond to real physical objects.
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