Abstract
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.
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Haro, J. The Schwinger Formula Revisited II (A Mathematical Treatment). International Journal of Theoretical Physics 43, 987–1001 (2004). https://doi.org/10.1023/B:IJTP.0000048596.81871.69
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DOI: https://doi.org/10.1023/B:IJTP.0000048596.81871.69