  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 vanishes 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
non-trivial electromagnetic and gravitational backgrounds with vanishing scalar
invariants. The implications of this result are discussed.
