https://doi.org/10.1140/epjc/s10052-023-11269-5
Regular Article - Theoretical Physics
Calculations of vacuum mean values of spinor field current and energy–momentum tensor in a constant electric background
1
Department of Physics, Tomsk State University, Lenin ave. 36, 634050, Tomsk, Russia
2
P.N. Lebedev Physical Institute, Leninskiy ave. 53, 119991, Moscow, Russia
3
Herzen State Pedagogical University of Russia, Moyka embankment 48, 191186, St. Petersburg, Russia
4
Institute of Physics, University of São Paulo, Rua do Matão, 1371, 05508-090, São Paulo, Brazil
a
breev@mail.tsu.ru
b
gavrilovsergeyp@yahoo.com
Received:
20
September
2022
Accepted:
24
January
2023
Published online:
2
February
2023
In the framework of strong-field QED with x-steps, we study vacuum mean values of the current density and energy–momentum tensor of the quantized spinor field placed in the so-called L-constant electric background. The latter background can be, for example, understood as the electric field confined between capacitor plates, which are separated by a sufficiently large distance L. First, we reveal peculiarities of nonperturbative calculating of mean values in strong-field QED with x-steps in general and, in the L-constant electric field, in particular. We propose a new renormalization and volume regularization procedures that are adequate for these calculations. We find necessary representations for singular spinor functions in the background under consideration. With their help, we calculate the above mentioned vacuum means. In the obtained expressions, we show how to separate global contributions due to the particle creation and local ones due to the vacuum polarization. We demonstrate how these contributions can be related to the renormalized effective Heisenberg–Euler Lagrangian.
© The Author(s) 2023
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