Vacuum polarization and particle production effects in classical electromagnetic and gravitational backgrounds 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 conjecture, by explicitly evaluating the effective Lagrangian, for nontrivial electromagnetic and gravitational backgrounds with vanishing scalar invariants. The implications of this result are discussed. © 1997 The American Physical Society.