Distributional Borel Summability for Vacuum Polarization by an External Electric Field
Emanuela Caliceti
TL;DR
This paper proves that the divergent perturbation series for vacuum polarization caused by a constant electric field is Borel summable in a distributional sense, providing a rigorous mathematical foundation for understanding pair production.
Contribution
It introduces a novel proof that the perturbation expansion in vacuum polarization is Borel summable in the distributional sense, advancing the mathematical understanding of quantum field effects.
Findings
Divergent series are Borel summable in the distributional sense.
Rigorous mathematical proof for vacuum polarization in an external electric field.
Enhanced understanding of pair production mechanisms.
Abstract
It is proved that the divergent perturbation expansion for the vacuum polarization by an external constant electric field in the pair production sector is Borel summable in the distributional sense.
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