The effect of point split regularization on the sign of the Casimir energy

Abstract: In a paper [1] the Casimir energy was calculated for a massive dirac field in (1+1) dimensional space-time in the presence of an inverse square well potential and shown to be positive. It will be shown that this result violates a key assumption of quantum field theory which is that the vacuum state is the state of minimum energy. The reason for this discrepancy is examined and is shown to be related to the way the charge density operator is defined. If the charge density operator is defined using point splitting then an extra term will be added to the charge which will result in the Casimir energy being negative.