static uniform or inhomogeneous electric fields was derived, in terms of instanton tunnelling through potential barriers in the space-dependent gauge, in @Kim02.

The Schwinger mechanism for particle production in a strong and uniform electric field for an infinite system was generalized to the case were the strong field is confined between two plates separated by a finite distance by @Wa88. The production rates, obtained by solving the Klein-Gordon and Dirac equations in a linear vector potential, can be expressed in an exact analytical form. The numerical evaluations of the production rates have shown large deviations from the Schwinger formula, thus indicating a large finite size effect in particle production. The explicit finite size corrections to the Schwinger formula for the rate of pair production for uniform electric fields confined to a bounded region were calculated, by using the Balian-Bloch expansion of the Green functions, by @Ma88 [@Ma89].

One important astrophysical situation in which electron-positron pair creation could play an extremely important role is the case of the electrosphere of the quark stars [@Us98a; @Us98b; @Us01; @PaUs02]. Quark stars could be formed as a result of a hadron-quark phase transition at high densities and/or temperatures [@It70; @Bo71; @Wi84]. If the hypothesis 