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الملخص الأصلي

كما كتبه المؤلفون، بالإنجليزية arXiv:2608.03747v1

We derive the leading logarithmic soft-photon theorem in $$d>4$$ spacetime dimensions and its classical radiative counterpart. A direct one-loop analysis in massive scalar quantum electrodynamics (QED) yields a factorizing soft term of order $$\omega^{d-4}\ln\omega$$, although the charged-particle S-matrix is infrared finite. The logarithm is generated by the scale-invariant loop-momentum region $$\omega\ll|\ell|\ll\Lambda$$, where $$\Lambda$$ denotes a characteristic hard-particle energy scale. At leading radiative order, the corresponding logarithmic contribution to the classical electromagnetic waveform arises from the long-range acceleration of the asymptotic charged particles. In even $$d\geq6$$, the straight-line waveform at this radiative order is distributionally supported in retarded time within an interval whose width is set by the characteristic size of the hard-scattering region, whereas the logarithmic acceleration term produces universal early- and late-time radiative tails proportional to $$|u|^{-(3d-10)/2}$$. In odd $$d\geq5$$, straight-line motion already gives a late-time tail at the same radiative order proportional to $$u^{-(d-4)/2}$$. The acceleration correction adds universal late- and early-time terms proportional, respectively, to $$\ln u/u^{(3d-10)/2}$$ and $$|u|^{-(3d-10)/2}$$. A comparison of Feynman and retarded boundary conditions separates the classically radiative contribution from the intrinsically quantum part of the logarithmic soft factor.