It is believed that in the presence of some strong electromagnetic fields, called overcritical, the (Dirac) vacuum becomes unstable and decays, leading to a spontaneous production of an electron-positron pair. However, most of the arguments are based on the analysis of static fields and are insufficient to explain this phenomenon completely. Therefore, we consider time-dependent overcritical fields and show, within the external field formulation, how spontaneous particle creation can be defined and measured in physical processes. We prove that the effect exists always when a overcritical field is switched on, but it becomes unstable and hence generically only approximate and non-unique when the field is switched on and off. In the latter case, it becomes unique and stable only in the adiabatic limit.
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