论文标题
经典的亚公开的软光子和四个时空尺寸的软重力定理
Classical Sub-subleading Soft Photon and Soft Graviton Theorems in Four Spacetime Dimensions
论文作者
论文摘要
经典的软光子和软重力定理决定了长波长电磁和重力波形，用于一般的经典散射过程，就电荷的电荷和iNgoing和宏观宏观对象的渐近矩而言。在频率变量中进行电磁和重力波形的傅立叶转化，可以在晚期和早期延迟时间发现电磁和重力波形。在这里，在\ cite {1912.06413}中开发的形式主义，我们得出了亚公开的电磁和引力波形，它们的表现就像$ u^{ - 2}（\ ln u）在四个时间间隔尺寸的早期和迟发时间$ $ $ $ $。我们还得出了亚公开的软光子定理，分析了标量QED中的两个循环幅度。最后，我们给出了对（sub）$^{n} $的领先非分析贡献的结构 - 领先的经典软光子和graviton定理，它们的表现就像$ u^{ - n}（\ ln u）^{n-1} $在早期和晚期弱智的时间$ u $中。
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 $u$.
