Regular Article - Theoretical Physics
Regularization, renormalization and consistency conditions in QED with x-electric potential steps
Department of Physics, Tomsk State University, 634050, Tomsk, Russia
2 P.N. Lebedev Physical Institute, 53 Leninskiy Prospect, 119991, Moscow, Russia
3 Department of General and Experimental Physics, Herzen State Pedagogical University of Russia, Moyka Embankment 48, 191186, St. Petersburg, Russia
4 Institute of Physics, University of São Paulo, CP 66318, CEP 05315-970, São Paulo, SP, Brazil
Accepted: 10 August 2020
Published online: 4 September 2020
The present article is an important addition to the nonperturbative formulation of QED with x-steps presented by Gavrilov and Gitman (Phys. Rev. D. 93:045002, 2016). Here we propose a new renormalization and volume regularization procedures which allow one to calculate and distinguish physical parts of different matrix elements of operators of the current and of the energy–momentum tensor, at the same time relating the latter quantities with characteristics of the vacuum instability. For this purpose, a modified inner product and a parameter of the regularization are introduced. The latter parameter can be fixed using physical considerations. In the Klein zone this parameter can be interpreted as the time of the observation of the pair-production effect. In the refined formulation of QED with x-steps, we succeeded to consider the back-reaction problem. In the case of an uniform electric field E confined between two capacitor plates separated by a finite distance L, we see that the smallness of the back-reaction implies a restriction (the consistency condition) on the product EL from above.
© The Author(s) 2020
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