Nontrivial classical backgrounds with vanishing quantum corrections

Abstract

Vacuum polarization and particle production effects in classical electromagnetic and gravitational back-grounds can be studied by the effective Lagrangian method. Background field configurations for which the effective Lagrangian is zero are special in the sense that the lowest order quantum corrections vanish for such configurations. We propose here the conjecture that there will be neither particle production nor vacuum polarization in classical field configurations for which all the scalar invariants are zero. We verify this conjec-ture, by explicitly evaluating the effective Lagrangian, for nontrivial electromagnetic and gravitational back-grounds with vanishing scalar invariants. The implications of this result are discussed.