between both half-pulses.

Similarly, we shall also consider a train consisting of $N_{\rm rep}$ such pulses, with $$F_{N_{\mathrm{rep}}}(t)=\mathcal{N}\sum_{\ell=1}^{N_{\mathrm{rep}}}F_1\Bigl[t+\Bigl(\ell-\frac{1}{2}(N_{\mathrm{rep}}+1)\Bigr)T\Bigr].
\label{a10}$$ Here, the normalization constant $\mathcal{N}$ is chosen such that $$\max_t |F_{N_{\mathrm{rep}}}(t)|=1,
\label{sg7}$$ to make sure that the maximum intensity of the electric field is independent of the parameters chosen in the above definitions. In Fig. \[dirackleinpola\], we represent the respective sequence of two pulses ($N_{\rm rep}=2$). Again, both columns in the figure are plotted for different values of $T_0$ (and $T$). This obviously has to influence the interference-diffraction pattern observed in the momentum distributions of created particles, the details of which will be presented in Sec. \[numerical\].

![The same as in Fig. \[dirackleinpolav2\] but for a sequence of two pulses \[$N_{\rm rep}=2$ in Eq. \]. In addition, we have $\sigma=20/t_C$, $T_0=200t_C$, $T=400t_C$ (left column), and $\sigma=10/t_C$, $T_0=10t_C$, $T=200t_C$ (right column). The remaining parameters of the field are the same as in Fig. \[dirackleinpolav2\]. \[dirackleinpola\]](dirackleinpola.eps){width="90.00000%"}

This model of the oscillating in time electric field will be used in Sec. \[numerical\] to illustrate the general theory derived in the next two sections. As first, we shall consider the bosonic pair creation. Its rigorous treatment is based on the Klein-Gordon equation, which is the 