https://doi.org/10.1140/epjc/s10052-020-8337-4
Regular Article - Theoretical Physics
Regularization, renormalization and consistency conditions in QED with x-electric potential steps
1
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
Received:
23
May
2020
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
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3
