An interesting result concerning the lower bound to the energy in the   Heisenberg picture
  In quantum theory it is generally assumed that there exists a special state called the vacuum state and that this state is a lower bound to the energy. However it has recently been demonstrated that this is not necessarily the case for some situations [5]. In order to clarify the situation we will consider a "very simple" field theory in the Heisenberg picture consisting of a quanitized fermion field with zero mass pariticles in 1-1D space-time interacting with a classical electrical potential. It will be shown that for this example there is no lower bound to the energy. 
Dan Solomon