  We calculate the cross sections for the production of one and more
electron-positron pairs due to the strong electromagnetic fields in
relativistic heavy ion collisions. Using the generating functional of fermions
in an external field we derive the N-pair amplitude. Neglecting the
antisymmetrisation in the final state we find that the total probability to
produce N pairs is a Poisson distribution. We calculate total cross sections
for the production of one pair in lowest order and also include higher-order
corrections from the Poisson distribution up to third order. Furthermore we
calculate cross sections for the production of up to five pairs including
corrections from the Poisson distribution.
