set of equations being solved for $c_{\bm p}^{(2)}(t)$ \[Eq.  for spinless particles ($s=0$) and Eq.  for spinor particles $(s=1/2)$\], we may observe different patterns in the momentum distributions . For instance, it was shown in Ref. [@Li1] that the longitudinal spectra of created bosons and fermions are shifted by $\pi/2$. In relation to those results, we will focus here on the longitudinal spectra as well, i.e., we set ${\bm p}_\perp={\bm 0}$. However, before presenting our numerical results we shall derive the Fraunhofer-type formulas for pair creation from vacuum that arise in the scalar and spinor QED.

Fraunhofer-type formulas for the scalar and spinor QED {#Fraunhoferform}
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Consider the time-evolution matrix ${\hat{U}}(t,t_0)$ for a single eigenmode of either the bosonic or fermionic field. In accordance with Eqs.  and , it satisfies the equation $${\mathrm{i}}\frac{{\mathrm{d}}}{{\mathrm{d}}t}{\hat{U}}(t,t_0)
=\begin{pmatrix} \omega_{\bm p}(t) & \mp{\mathrm{i}}\Omega_{\bm p}(t) \cr -{\mathrm{i}}\Omega_{\bm p}(t) & -\omega_{\bm p}(t) \end{pmatrix}
{\hat{U}}(t,t_0),
\label{res2}$$ where the upper sign relates to the boson and the lower one to the fermion statistics. Note that $\Omega_{\bm p}(t)$ differs in both cases too \[Eqs.  and \]. It follows from  that for fermions the time evolution is unitary, meaning that ${\hat{U}}$ belongs to the $SU(2)$ group (see, Appendix \[appendix1\]). However, for 