Closed-form weak-field expansion of two-loop Euler-Heisenberg Lagrangians

Abstract

We obtain closed-form expressions, in terms of the Faulhaber numbers, for the weak-field expansion coefficients of the two-loop Euler-Heisenberg effective Lagrangians in a magnetic or electric field. This follows from the observation that the magnetic worldline Green's function has a natural expansion in terms of the Faulhaber numbers. © SISSA 2006.