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Two-loop self-dual Euler-Heisenberg Lagrangians (I): Real part and helicity amplitudes

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arxiv hep-th/0205004 v2 pith:2BUM4S4N submitted 2002-04-30 hep-th hep-phmath-phmath.MP

classification hep-thhep-phmath-phmath.MP
keywords helicityresultstwo-loopamplitudeseffectiveeuler-heisenberglagrangiansscalar
verification ladder T0 review T1 audit T2 compute T3 formal
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We show that, for both scalar and spinor QED, the two-loop Euler-Heisenberg effective Lagrangian for a constant Euclidean self-dual background has an extremely simple closed-form expression in terms of the digamma function. Moreover, the scalar and spinor QED effective Lagrangians are very similar to one another. These results are dramatic simplifications compared to the results for other backgrounds. We apply them to a calculation of the low energy limits of the two-loop massive N-photon `all +' helicity amplitudes. The simplicity of our results can be related to the connection between self-duality, helicity and supersymmetry.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Scattering and depletion in a flying focus from conformal transformations

    hep-ph 2026-05 unverdicted novelty 7.0 of 10

    Photon emission amplitudes in totally depleting flying focus beams equal a Gaussian average over momentum variables of the corresponding plane-wave amplitudes, obtained via conformal transformations of Volkov solutions.

  2. Worldline representation of multiloop amplitudes in quantum electrodynamics

    hep-th 2026-07 conditional novelty 5.0 of 10

    Worldline master integrals combine whole classes of QED Feynman diagrams and yield new coefficients for the two-loop scalar QED vacuum polarization.

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