Exact Evaluation and Resummation of the Divergent Expansion for the Heisenberg-Euler Lagrangian
We devise a novel resummation prescription based on the method of finite-part integration [Galapon EA. 2017 Proc. R. Soc A 473, 20160567. (doi:10.1098/rspa.2016.0567)] to perform a constrained extrapolation of the divergent weak-field perturbative expansion for the Heisenberg-Euler Lagrangian to the...
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| Main Authors: | , , |
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| Format: | text |
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Archīum Ateneo
2025
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| Online Access: | https://archium.ateneo.edu/physics-faculty-pubs/182 https://doi.org/10.1098/rspa.2024.0843 |
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| Summary: | We devise a novel resummation prescription based on the method of finite-part integration [Galapon EA. 2017 Proc. R. Soc A 473, 20160567. (doi:10.1098/rspa.2016.0567)] to perform a constrained extrapolation of the divergent weak-field perturbative expansion for the Heisenberg-Euler Lagrangian to the non-perturbative strong magnetic and electric field regimes. In the latter case, the prescription allowed us to reconstruct the non-perturbative imaginary part from a finite collection of the real expansion coefficients. We also demonstrate the utility of the various equivalent representations of Hadamard's finite part in deriving the exact closed form for the Heisenberg-Euler Lagrangian from the non-perturbative integral representation. |
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