发表机构
Institute of Physics “Gleb Wataghin”, University of Campinas — UNICAMP（坎皮纳斯大学（UNICAMP）“格列布·瓦塔金”物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究四维引力散射中软对数定理对大质量粒子轨迹的修正，分离度规影响并证明非线性源仅通过特定模式作用，用勒让德多项式求得$G$领头阶各对数阶系数，前两阶与已知结果一致。
AI 中文摘要
我们研究了大质量粒子渐近轨迹的对数修正。这些修正进入四维引力散射中零无穷远处辐射场的软对数扇区的计算。我们首先分离出进入粒子运动方程的度规部分。我们证明非线性源只能通过双曲面上的齐次模式影响该扇区，并且与所提出的软塔匹配意味着这些模式消失，除了第一个模式。我们证明该模式在$G$领头阶下不能影响轨迹系数。然后我们在粒子世界线上反转物质能量-动量张量，以使用勒让德多项式获得$G$领头阶和每个对数阶的轨迹系数。前两个系数重现了在$G$和$G^2$阶的已知结果。
英文摘要
We study the logarithmic corrections to the asymptotic trajectories of massive particles. These corrections enter the calculation of the soft-log sector of the radiative field at null infinity in four-dimensional gravitational scattering. We first isolate the part of the metric which enters the particle equations of motion. We show that the nonlinear source can only affect this sector through homogeneous modes on the hyperboloid, and that matching to the proposed soft tower implies that these modes vanish, except for the first mode. We show that this mode cannot affect the trajectory coefficients at leading order in G. We then invert the matter energy-momentum tensor on the particle worldlines to obtain the trajectory coefficients at leading order in $G$ and at every logarithmic order using Legendre polynomials. The first two coefficients reproduce the known results at orders $G$ and $G^2$. .
Comments18 pages
