The Schwinger formula revisited II (a mathematical treatment).
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In this paper we study the production of pairs in no-analytic potentials. It is a well-known fact that, when the potential is analytic the average number of produced pairs is exponentially small in ?. On the other hand, when the potential is no-analytic, using the W.K.B. method, we prove that the average number of produced pairs is ?????, where ? is the regularity of the potential and ? is the fine structure constant. Finally, we give a rigorous proof of the Schwinger’s formula.