and for $\sigma=10/t_C$, $T_0=10t_C$ (right column). In both cases, the amplitude of the electric field is $\mathcal{E}_0=-0.1\mathcal{E}_S$. Also, the dashed lines are for $M=1$, whereas the solid lines are for $M=5$. As one can see, with increasing $M$, the shape of super-Gaussian envelopes becomes similar to the rectangular one. The qualitative difference between both columns is that, while in the left column both half-pulses are well separated in time, in the right column they overlap. In other words, the single pulse in the left column is much longer that the one on the right. As we will show later, this will strongly affect the structure of diffraction patterns observed in the momentum distributions of created pairs. \[dirackleinpolav2\]](dirackleinpolav2.eps){width="90.00000%"}

We consider an electric field which oscillates linearly along the $z$-direction, ${\mathbfcal{E}}(t)={\cal E}(t){\bm e}_z$. In addition, we assume that it satisfies the condition, $$\int_{-\infty}^{+\infty}{\mathrm{d}}t\,{\cal E}(t)=0.
\label{a2}$$ If the electric field is defined as $${\cal E}(t)={\cal E}_0F(t),
\label{a3}$$ where ${\cal E}_0$ is the field amplitude whereas $F(t)$ is its shape function, then it follows from  that $$\int_{-\infty}^{+\infty}{\mathrm{d}}t\,F(t)=0.
\label{a4}$$ The significance of Eqs.  and  becomes clear when we introduce the vector potential; namely, ${\bm A}(t)=A(t){\bm e}_z$ where ${\cal E}(t)=-{\rm d}A(t)/{\rm d}t$. In other words, if 