Vacuum Polarization Effects from Fermion Zero-Point Energy
  The influence of an external electromagnetic field on the vacuum structure of a quantized Dirac field is investigated by considering the quantum corrections to classical Maxwell's lagrangian density induced by fluctuations of the non-perturbative vacuum. Effective Lagrangian densities for Maxwell's theory in (3+1) and (2+1) dimensions are derived from the vacuum zero-point energy of the fermion field in the context of a consistent Pauli-Villars-Rayski subtraction scheme, recovering Euler-Kockel-Heisenberg and Maxwell-Chern-Simons effective theories. Effective scalar quantum electrodymanics as well as low temperature effects in both spinor and scalar theories are also discussed. 
J.L. Tomazelli