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Classical Sub-subleading Soft Photon and Soft Graviton Theorems in Four Spacetime Dimensions

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arxiv 2008.04376 v3 pith:UV7R5SMS submitted 2020-08-10 hep-th gr-qc

Biswajit Sahoo This is my paper · ORCID
classification hep-thgr-qc
keywords softclassicalelectromagneticgravitationalphotonwaveformsearlygraviton
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abstract

Classical soft photon and soft graviton theorems determine long wavelength electromagnetic and gravitational waveforms for a general classical scattering process in terms of the electric charges and asymptotic momenta of the ingoing and outgoing macroscopic objects. Performing Fourier transformation of the electromagnetic and gravitational waveforms in the frequency variable one finds electromagnetic and gravitational waveforms at late and early retarded time. Here extending the formalism developed in \cite{1912.06413}, we derive sub-subleading electromagnetic and gravitational waveforms which behave like $u^{-2}(\ln u)$ at early and late retarded time $u$ in four spacetime dimensions. We also have derived the sub-subleading soft photon theorem analyzing two loop amplitudes in scalar QED. Finally, we give the structure of leading non-analytic contribution to (sub)$^{n}$-leading classical soft photon and graviton theorems which behave like $u^{-n}(\ln u)^{n-1}$ for early and late retarded time $u$.

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Cited by 4 Pith papers

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

  1. Logarithmic Soft Photon Theorem and Waveform Tails in Higher Dimensions

    hep-th 2026-08 conditional novelty 7.0 of 10

    In d>4, soft photon emission acquires a universal omega^{d-4} ln omega factor, producing power-law early- and late-time radiative tails in the classical electromagnetic waveform.

  2. Memory effect from the scattering of Taub-NUT black holes

    hep-th 2026-03 conditional novelty 7.0 of 10

    Soft theorems yield a gauge-invariant nutty soft factor and the associated memory tensor for Kerr-Taub-NUT scattering, with magnetic components and directional divergences absent in electromagnetism.

  3. Subleading soft radiation during scattering of dressed states in QED

    hep-th 2025-11 conditional novelty 4.0 of 10

    With subleading-corrected Faddeev-Kulish dressing, tree-level QED bremsstrahlung below the dressing scale vanishes, and elastic dressed amplitudes equal the infrared-finite part of Fock amplitudes.

  4. Celestial Chiral Algebras and Self-Dual Gravity

    hep-th 2025-07 conditional novelty 4.0 of 10

    This thesis derives deformations of celestial chiral algebras in self-dual gravity on curved backgrounds, obtaining W(infinity) on Eguchi-Hanson space, Ldiff_q(C) under Moyal deformation, and a two-parameter deformati...

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