Relationship of the pair creation yield during and after the interaction

We compare the predictions of two different approaches of studying the electron–positron pair creation process triggered by a supercritical field inside the interaction region before the field is turned off. These two approaches are based on the projection of the electron–positron field operator on the sub-space spanned by either field-free or instantaneous energy eigenstates. For the case of an infinitely extended static electric field, we suggest that the type of the chosen turn-off of the external field determines which of the two approaches is physically more meaningful. We also derive an alternative quantum kinetic Vlasov equation, which is more meaningful than the traditional one to predict the interaction if the field is turned off sufficiently rapidly. (paper)