Exact Evaluation and Resummation of the Divergent Expansion for the Heisenberg-Euler Lagrangian

• المؤلفون الرئيسيون: Tica, Christian D., Blancas, Philip Jordan D, Galapon, Eric A.
• التنسيق: text
• منشور في: Archīum Ateneo 2025
• الموضوعات: divergent integral; Hadamard's finite part; perturbation; Physical Sciences and Mathematics; Physics
• الوصول للمادة أونلاين: https://archium.ateneo.edu/physics-faculty-pubs/182; https://doi.org/10.1098/rspa.2024.0843
• المؤسسة: Ateneo De Manila University

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.