Particle creation and vacuum polarization by a nonstationary electric field

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.