(see, for instance, Refs. [@Peng; @Feng]). As we show in this paper, the exceptional points are also found in the dynamical pair production of spin 0 particles, and it is only at those points that the fully coherent enhancement of the respective particle spectra is observed. Note that our problem relies on studying a two-state dynamics. Therefore, the conclusions drawn from our results apply essentially to any system such that its dynamics can be traced back to that of a two-level system.

The paper is organized as follows. In Sec. \[theory\], we shall present the theoretical formulation of the dynamical Sauter-Schwinger process using either the scalar or spinor QED. Momentum distributions of created pairs based on both these theories will be presented in Sec. \[results\]. Also in Sec. \[results\], we will provide an analytical explanation of our numerical results arising from the analysis of the operators that evolve in time bosonic and fermionic fields. The properties of those operators will be analyzed in Appendix \[SU(1,1)\] and \[appendix1\], respectively. In Sec. \[conclusions\], we will summarize our results.

The numerical results will be expressed in relativistic units. Specifically, we shall use the Sauter-Schwinger electric field strength $\mathcal{E}_S=m_{\mathrm{e}}^2c^3/|e|\hbar$, with the corresponding strength of 