On the application of the Kramers-Kronig relations to the interaction timeproblem

It is shown that the two components of the complex characteristic interacti on time tau(omega) = tau(1)(omega) - i tau(2)(omega) for classical electrom agnetic waves with an arbitrary shaped barrier are not entirely independent quantities, but are connected by the Kramers-Kronig relations. The corresp onding macroscopic sum rule for the complex time is also derived. An analog y between the interaction time problem and an electrical circuit with capac itive and conducting components is established from which we propose that t he effective crossing time should be the maximum of the two components.