Closed-form two-loop Euler-Heisenberg Lagrangian in a self-dual background

Abstract

We show that the two-loop Euler-Heisenberg effective Lagrangian for scalar QED in a constant Euclidean self-dual background has a simple explicit closed form expression in terms of the digamma function. This result leads to a simple analysis of the weak- and strong-field expansions, the two-loop scalar QED beta function, and the analytic continuation properties of the effective Lagrangian and its imaginary part.

8 pages, latex

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• On the Higher Loop Euler-Heisenberg Trans-Series Structure
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• Reducible contributions to quantum electrodynamics in external fields
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• Black Hole Entropy, Quantum Corrections and EFT Transitions
• Spinning Particles in Quantum Mechanics and Quantum Field Theory
• Non-Perturbative One-Loop Effective Action for QED with Yukawa Couplings
• Closed-form weak-field expansion of two-loop Euler-Heisenberg Lagrangians
• Studies of low-energy effective actions in supersymmetric field theories
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• Dihedral Invariant Polynomials in the effective Lagrangian of QED