Fermion-antifermion pair-production in the presence of classical fields is
described based on the retarded and advanced fermion propagators. They are
obtained by solving the equation of motion for the Dirac Green's functions with
the respective boundary conditions to all orders in the field. Subsequently,
various approximation schemes fit for different field configurations are
explained. This includes longitudinally boost-invariant forms. Those occur
frequently in the description of ultrarelativistic heavy-ion collisions in the
semiclassical limit. As a next step, the gauge invariance of the expression for
the expectation value of the number of produced fermion-antifermion pairs as a
functional of said propagators is investigated in detail. Finally, the
calculations are carried out for a longitudinally boost-invariant model-field,
taking care of the last issue, especially.Comment: 32 pages, 8 figures, revised versio