从探针振幅到所有阶的径向作用量
The Radial Action from Probe Amplitudes to All Orders
AI总结：
该工作从散射振幅中提取了探针极限下所有阶的经典相对论径向作用量，涵盖点电荷、磁单极子及史瓦西和纯NUT背景，并展示了纯NUT散射振幅由连分数超越方程解出，可求解至任意圈阶。
摘要：
我们在微扰论的所有阶上，从散射振幅中提取了相对论性的经典径向作用量，在探针极限下进行。我们的源包括点电荷和磁单极子，以及史瓦西和纯NUT引力背景。一个典型的相对论效应，即散射轨迹可能绕这些源任意多次，可以在获得所有阶振幅时恢复。我们表明，探针在纯NUT上散射的振幅由一个涉及连分数的超越方程的解给出，并解释了如何将该方程求解到任意所需的圈阶。
英文摘要：
We extract the relativistic classical radial action from scattering amplitudes, to all orders in perturbation theory, in the probe limit. Our sources include point charges and monopoles, as well as the Schwarzschild and pure-NUT gravitational backgrounds. A characteristic relativistic effect, that scattering trajectories may wind around these sources any number of times, can be recovered when all-order amplitudes are available. We show that the amplitude for scattering a probe off a pure NUT is given by the solution of a transcendental equation involving continued fractions, and explain how to solve this equation to any desired loop order.
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