A glimpse on higher-loop contributions to the Heisenberg-Euler effective action

by Felix Karbstein

Thursday 19 Dec 2024, 14:15 → 15:45 Europe/Berlin

Abbeanum/Ground floor-HS 2 - Hörsaal 2 (TPI, FSU Jena)

In an attempt to obtain any controlled insights into the low-energy effective theory governing the physics of classical electromagnetic fields in the quantum vacuum beyond low loop orders, we study the Heisenberg-Euler effective action in constant electromagnetic fields $\bar{F}$ for quantum electrodynamics (QED) with $N$ charged particle flavors of the same mass and charge $e$ in the large $N$ limit characterized by sending $N \to \infty$ while keeping $Ne^2 \sim e \bar{F} \sim N^0$ fixed. This immediately implies that contributions that scale with inverse powers of $N$ can be neglected and the resulting effective action scales linearly with $N$. Interestingly, due to the presence of one-particle reducible diagrams, even in this specific limit the Heisenberg-Euler effective action receives contributions of arbitrary loop order. In particular for the special cases of electric- and magnetic-like field configurations we construct an explicit expression for the associated effective Lagrangian that, upon extremization for two constant scalar coefficients, allows to evaluate its full, all-order result at arbitrarily large field strengths. We also comment on relations to physically realized $N = 1$ QED.