Adiabatic Pair Creation

We give here the proof that pair creation in a time dependent potentials is possible. It happens with probability one if the potential changes adiabatically in time and becomes overcritical, that is when an eigenvalue enters the upper spectral continuum. The potential may be assumed to be zero at large negative and positive times. The rigorous treatment of this effect has been lacking since the pioneering work of Beck, Steinwedel and Suessmann in 1963 and Gershtein and Zeldovich in 1970.