AI 中文总结
本文在自力有效场论中研究高能激波散射，计算1SF阶波形至后闵可夫斯基所有阶，证明超普朗克区域首阶消失及共线辐射能量角谱的紫外有限性。
AI 中文摘要
我们在自力有效场论框架内研究两个无自旋体的高能碰撞，取其中一个体为无质量且高能，从而产生引力激波背景。该激波受到第二个体的扰动，第二个体可为无质量或有质量，分别满足$E_2/E_1\ll1$或$m_2/E_1\ll1$。尽管激波的自力展开依赖于参考系，我们选择了一个使该有效场论充分发挥其威力的参考系，从而获得对牛顿常数所有阶都有效的结果，并使得潜在的求和重排模式得以显现。具体而言，我们将展开推进到1SF阶，并猜想在给定规范中所谓的反冲算符在所有阶上消失。我们获得了激波背景上的精确引力子传播子，与先前结果一致，并利用它计算了动量空间中1SF阶的壳上波形，专门针对无质量-无质量碰撞。该波形在后闵可夫斯基展开的所有阶上计算，其求和重排形式被证明在超普朗克区域的首阶消失。我们利用这一结果证明了在与能量为$E_1$的激波共线区域内辐射能量角谱的紫外有限性。
英文摘要
We investigate the high-energy collision of two spinless bodies within the Self-Force Effective Field Theory, taking one of the two bodies to be massless and highly energetic, such that it generates a gravitational shockwave (GSW) background. The GSW is perturbed by a second body, either massless or massive, satisfying respectively $E_2/E_1\ll1$ or $m_2/E_1\ll1$. Although the Self-Force expansion for shockwaves is frame-dependent, we choose a frame in which this EFT manifests its full power, obtaining results valid to all orders in Newton's constant that make the underlying resummation patterns manifest. Specifically, we push the expansion to 1SF order and conjecture the all-order vanishing of the so-called recoil operators in a given gauge. We obtain the exact graviton propagator on the shockwave background, matching previous results, and use it to compute the on-shell waveform at 1SF order in momentum space, specialising to the massless-massless collision. The waveform is computed to all orders in the Post-Minkowskian expansion, and its resummed form proved to vanish at the leading order in the super-Planckian regime. We use this result to prove the UV finiteness of the angular spectrum of radiated energy in the region collinear to the shockwave with energy $E_1$.
Comments49 pages, 5 figures
