Pair production in external field as a tunneling process

Quantum electrodynamics predicts that super-strong electric fields would create e(+)e(-)-pairs from the vacuum. The process has never been observed, since the fields required are not yet attainable. The paper contains a review of the general theory and of the results obtained for spatially uniform and time-dependent electric fields. However, in order to apply the theory to processes which may take place at the focus of a laser beam, the effects of the field space dependence should be taken into account. The pair creation is forbidden classically and may be considered as a tunneling. The corresponding semi-classical arguments provide with an estimate in agreement with the exact quantum theory, but both have been developed until now for uniform fields only.