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arXiv 2008.04376hep-thgr-qc
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四维时空中的经典次次导软光子和软引力子定理

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

Biswajit Sahoo

摘要:

经典的软光子和软引力子定理确定了一般经典散射过程的长波长电磁和引力波形,这些波形是由进出宏观物体的电荷和渐近动量决定的。在频率变量中执行电磁和重力波形的傅立叶变换,可以找到延迟时间的晚期和早期的电磁和重力波形。在这里扩展的形式主义在\cite{1912.06413},我们推导出子subleading电磁和引力波形的行为像$u^{-2}(\ln u)$在早期和晚期延迟时间$u$在四维时空。我们还导出了标量QED中分析两个圈振幅的次次引导软光子定理。最后,给出了对(子)$^{n}$的主导非解析贡献的结构--主导经典软光子和引力子定理,它们在延迟时间$u$的早期和晚期表现出类似于$u^{-n}(\ln u)^{n-1}$的性质.

英文摘要:

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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