Search for periodic vacuum in QED(2)

It is shown that the vacuum of QED(2) in Minkowski spacetime does not favou r a periodic electric mean field. The projected effective action exhibiting a genuine dependence on the non-vanishing background field has been introd uced. The functional dependence of the energy density of the vacuum on the assumed periodic vacuum expectation value of the vector potential is determ ined from the component T-00 of the energy-momentum tensor at one-loop orde r. Treating the background field non-perturbatively, the energy of the vacu um in the presence of a periodic mean field is found not to be equal to the negative of the effective action.