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.

12 pages

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Cited by in corpus (3)

• Euler-Heisenberg lagrangians and asymptotic analysis in 1+1 QED, part 1: Two-loop
• Three-loop Euler-Heisenberg Lagrangian in 1+1 QED, part 1: single fermion-loop part
• Large quark mass Euler-Heisenberg type action for QCD with quark sources and its Abelian limit