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.
Two-loop self-dual Euler-Heisenberg Lagrangians (I): Real part and helicity amplitudes
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abstract
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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Scattering and depletion in a flying focus from conformal transformations
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.