Iwo Bialynicki-Birula, Lukasz Rudnicki
Exact analytical solutions are presented for the time evolution of the
density of pairs produced in the QED vacuum by a uniform electric field that is
adiabatically switched on starting at -infinity. Pair production is described
by the Dirac-Heisenberg-Wigner function introduced before [Phys. Rev. D 44,
1825 (1991)]. The explicit solution is obtained by an extension of the method
of the spinorial decomposition to deal with a time-varying electric field. The
main result of this work is that the pair density as a function of the field
strength can be expanded into a power series. The essential singularity present
in the Schwinger formula must be, therefore, attributed to the infinitely long
duration of the process of pair creation by a time-independent feld or
alternatively by an abrupt switching of the field.
View original:
http://arxiv.org/abs/1108.2615
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