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Low-energy limit of N-photon amplitudes in a constant field

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arxiv 2312.07047 v1 pith:4ICQNQAT submitted 2023-12-12 hep-th hep-ph

Low-energy limit of N-photon amplitudes in a constant field

classification hep-th hep-ph
keywords amplitudeslow-energyn-photonconstantfieldlevellimitonly
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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While the QED photon amplitudes at full momentum so far have been calculated only up to the six-photon level, in the low-energy limit there are explicit formulas for all helicity components even at the N-photon level, obtained by Martin et al. in 2002. Here we use the worldline formalism to extend that result to the N-photon amplitudes in a generic constant field. For both scalar and spinor QED, we obtain compact representations for the low-energy limits of these amplitudes involving only simple algebra and a single global proper-time integral with trigonometric integrand.

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