The Schwinger Formula Revisited II (A Mathematical Treatment)

We study the production of pairs in non-analytic potentials. While, when the potential is analytic, the average number of produced pairs is exponentially small in ħ, when the potential is non-analytic, using the W.K.B. method, we prove that the average number of produced pairs is $$\mathcal{O}$$ (αħ 2N ), where N is the regularity of the potential and α is the fine structure constant. We give a rigorous proof of the Schwinger's formula.