  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 external
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.
