标题： 引力波物理中的经典振幅 显示英文标题

标题： Classical Amplitudes in Gravitational-Wave Physics

摘要： 在本论文中，我们研究了尾部类非线性过程的发射振幅，这些过程属于$G_N^2$阶，并代表了散射引力辐射与静态背景曲率的效应，包括不仅质量尾部，还有由于源的角动量导致的“失败”尾部。 正如我们在工作中最初所展示的，其中一些振幅表现出异常，这些异常随后通过具有传统方法直接对应关系的场论工具得到了正确理解和修正。 我们还研究了发射与自能图之间的关系，并特别表明，为了正确考虑来自辐射过程的保守项，有必要对异常自能图进行修正。 由此，我们获得了来自电四极角动量失败尾部的保守 5PN 的正确贡献，修正了文献中的先前结果。 此外，我们首次计算了任意多极矩下角动量失败尾部的保守贡献。 随后，我们探讨了质量尾部的自然高阶扩展（阶数为$G_N^3$），称为尾部的尾部，适用于一般的电和磁多极矩。 正如我们将看到的，遇到了长距离和短距离发散，这些发散随后通过标准的重整化技术得到了正确的理解和处理。 在这种情况下，我们能够通过积分重整化群方程来重求和对数贡献。 因此，在本论文中，我们扩展了涉及辐射模式和势模式混合过程的特别棘手区域的后牛顿微扰展开。 显示英文摘要

摘要： In this thesis, we study emission amplitudes for the class of nonlinear processes of tails, which are processes of order $G_N^2$, and represent the effect of scattering gravitational radiation off the static background curvature, including not only mass tails but also the "failed" tails due to the angular momentum of the source. As originally shown in our work, some of these amplitudes present anomalies, which are then properly understood and corrected with field theory tools which have straightforward counterpart in traditional methods. We also investigate the relation between emission and self-energy diagrams and, in particular, show that a correction to the anomalous self-energy diagrams is necessary to correctly account for conservative terms that arise from radiative processes. From this, we obtain the correct contribution to the conservative 5PN stemming from the electric quadrupole angular momentum failed tail, correcting previous results in the literature. Besides this, we also compute for the first time the conservative contributions from the angular momentum failed tail, for arbitrary multipole moments. Subsequently, we explore the natural higher-order extension (of order $G_N^3$) of the mass tails, called tails of tails, for generic electric and magnetic multipoles. As we will see, both long- and short-distance divergences are encountered, which are then properly understood and dealt with in terms of standard renormalization techniques. In this case, we are able to resum the logarithmic contributions through the integration of the renormalization group equation. Thus, in this thesis, we have extended the post-Newtonian perturbative expansion in the particularly thorny region of processes involving the mixture of radiative and potential modes.