Self-consistent relativistic random phase approximation with vacuum   polarization
  We present a theoretical formulation for the description of nuclear excitations within the framework of relativistic random-phase approximation whereby the vacuum polarization arising from nucleon-antinucleon fields is duly accounted for. The vacuum contribution to Lagrangian is explicitly described as extra new terms of interacting mesons by means of the derivative expansion of the effective action. It is shown that the self-consistent calculation yields zero eigenvalue for the spurious isoscalar-dipole state and also conserves the vector-current density. 
A. Haga, H. Toki, S.Tamenaga, Y. Horikawa, and H. L. Yadav