Geodesic
Particle creation and vacuum polarization by a~nonstationary electric field
Teoretičeskaâ i matematičeskaâ fizika, Tome 45 (1980) no. 2, pp. 210-223

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Method of calculating the vacuum polarization of scalar and spinor fields by the homogeneous electric field $E(t)$ with an arbitrary time dependence is suggested. With the help of this method the expressions are found for the total vacuum stress-energy tensor and current of guantized fields in the external electric field of a special type. Under the conditions $k_0\ll m$, $E\ll E_\text{cr}$ the calculation of the vacuum polarization by an arbitrary non-stationary electric field is performed. It is shown that for optical frequencies $k_0\sim 10^{-6}$ the contribution to the polarization energy density from the terms which depend on $E'$, $E''$ is much larger than that of the Heisenberg–Euler terms. 
@article{TMF_1980_45_2_a5,
     author = {V. M. Mostepanenko},
     title = {Particle creation and vacuum polarization by a~nonstationary electric field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {210--223},
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_45_2_a5/}
}
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V. M. Mostepanenko. Particle creation and vacuum polarization by a~nonstationary electric field. Teoretičeskaâ i matematičeskaâ fizika, Tome 45 (1980) no. 2, pp. 210-223. http://geodesic.mathdoc.fr/item/TMF_1980_45_2_a5/