Exact Evaluation and Resummation of the Divergent Expansion for the Heisenberg-Euler Lagrangian - Tica, Christian D. (Archīum Ateneo, 2025)
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.