Some remarks on point split commutators
  Point splitting has been suggested as a way to deal with anomalous commutators in quantum field theory. It has been pointed out by D.G. Boulware[4] that in order to obtain a mathematically consistent theory the Hamiltonian operator must be point split also. We will examine the effect of point splitting the Hamiltonian for a free fermion field in 1-1D space-time. It will be shown that when the Hamiltonian operator is point split then quantum states will exist with less energy than the normal vacuum state. This requires the vacuum state to be redefined. 
Dan Solomon