This review article presents the progress made over the last decade, since the introduction of effective field theories (EFTs) into post-Newtonian (PN) Gravity. These have been put forward in the context of gravitational waves (GWs) from the compact binary inspiral. The mature development of this interdisciplinary field has resulted in significant advances of wide interest to physics at several levels serving various purposes. The field has firmly demonstrated, that seemingly disparate physical domains, such as quantum field theory (QFT) and classical Gravity, are related, and that the EFT framework is a universal one, where it has proved to supply a robust methodology to boost the progress in PN theory. In this review emphasis was put on an accessible pedagogic presentation of the field theoretic aspects of the subject, with the view, that these are in fact common across the whole of theoretical physics, rather than in their original narrow quantum context. The review is aimed at a broad audience, from general readers new to the field, to specialists and experts in related subjects. The review begins with an overview of the introduction of EFTs into classical Gravity and their development. Then, the basic ideas, which form the conceptual foundation of EFTs, are provided, and the strategy of a multi-stage EFT framework, which is deployed for the PN binary inspiral problem, is outlined. The main body of the review is then dedicated to presenting in detail the study of each of the effective theories at each of the intermediate scales in the problem, up to the actual GW observables. First, the EFT for a single compact object is considered, from which one proceeds to the EFT of a compact binary system, viewed as a composite particle with internal binding interactions. Finally, one arrives at the effective theory of the time dependent multipole moments of the radiating system. The review is concluded with the multiple prospects of building on the field, and using further modern field theory insights and tools, to address specifically the study of GWs, as well as to broadly expand our fundamental understanding of gauge and Gravity theories across the classical and quantum regimes.

中文翻译：

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后牛顿引力的有效场论：综合回顾

这篇评论文章介绍了自将有效场理论 (EFT) 引入后牛顿 (PN) 引力以来在过去十年中取得的进展。这些是在来自紧凑双星螺旋的引力波 (GW) 的背景下提出的。这一跨学科领域的成熟发展导致了物理学在多个层次上的广泛关注的重大进展，用于各种目的。该领域已经坚定地证明，看似不同的物理领域，如量子场论 (QFT) 和经典引力，是相关的，并且 EFT 框架是一个通用框架，它已被证明提供了一种强大的方法来促进进展在 PN 理论中。在这篇评论中，重点放在了该主题领域理论方面的易于理解的教学方法上，认为，这些实际上在整个理论物理学中都很常见，而不是在它们最初的狭隘量子环境中。该评论面向广泛的受众，从该领域的新读者到相关学科的专家和专家。该评论首先概述了将 EFT 引入经典 Gravity 及其发展的概述。然后，提供了构成 EFT 概念基础的基本思想，并概述了为 PN 二元启发问题部署的多阶段 EFT 框架的策略。然后，评论的主体致力于详细介绍对问题中每个中间尺度上的每个有效理论的研究，直到实际的 GW 可观测值。首先，考虑单个紧凑对象的 EFT，一个紧凑的二元系统的 EFT，被视为具有内部结合相互作用的复合粒子。最后，我们得出了辐射系统随时间变化的多极矩的有效理论。该评论的结论是建立在该领域的多种前景，并使用进一步的现代场论见解和工具，专门解决 GW 的研究，并广泛扩展我们对经典和引力理论的基本理解。量子体制。