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The present article is an important addition to the nonperturbativeformulation of QED with x-steps presented by Gavrilov and Gitman in Phys. Rev.D. 93, 045002 (2016). Here we propose a new renormalization and volumeregularization procedures which allow one to calculate and distinguish physicalparts of different matrix elements of operators of the current and of theenergy-momentum tensor, at the same time relating the latter quantities withcharacteristics of the vacuum instability. For this purpose, a modified innerproduct and a parameter {\tau} of the regularization are introduced. The latterparameter can be fixed using physical considerations. In the Klein zone thisparameter can be interpreted as the time of the observation of the pairproduction effect. In the refined formulation of QED with x-steps, we succeededto consider the backreaction problem. In the case of an uniform electric fieldE confined between two capacitor plates separated by a finite distance L, wesee that the smallness of the backreaction implies a restriction (theconsistency condition) on the product EL from above.

Regularization, renormalization and consistency conditions in QED with x-electric potential steps