Abstract
We show that the leading derivative corrections to the Heisenberg-Euler effective action can be determined efficiently from the vacuum polarization tensor evaluated in a homogeneous constant background field. After deriving the explicit parameter-integral representation for the leading derivative corrections in generic electromagnetic fields at one loop, we specialize to the cases of magnetic- and electric-like field configurations characterized by the vanishing of one of the secular invariants of the electromagnetic field. In these cases, closed-form results and the associated all-orders weak- and strong-field expansions can be worked out. One immediate application is the leading derivative correction to the renowned Schwinger-formula describing the decay of the quantum vacuum via electron-positron pair production in slowly-varying electric fields.
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Karbstein, F. Derivative corrections to the Heisenberg-Euler effective action. J. High Energ. Phys. 2021, 70 (2021). https://doi.org/10.1007/JHEP09(2021)070
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DOI: https://doi.org/10.1007/JHEP09(2021)070