We calculate the motion of binary mass systems in gravity up to the fourth post–Newtonian order. We use momentum expansions within an effective field theory approach based on Feynman amplitudes in harmonic coordinates by applying dimensional regularization. We construct the canonical transformations to ADM coordinates and to effective one body theory (EOB) to compare with other approaches. We show that intermediate poles in the dimensional regularization parameter ε vanish in the observables and the classical theory is not renormalized. The results are illustrated for a series of observables for which we agree with the literature.

中文翻译：

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基于有效场论方法的四体系统的第四次牛顿后哈密顿动力学

我们计算重力下二元质量系统的运动，直至第四次牛顿阶。通过应用尺寸正则化，我们在谐波坐标中基于费曼振幅的有效场论方法中使用了动量展开。我们构造了对ADM坐标和有效的一个人体理论（EOB）的规范转换，以与其他方法进行比较。我们表明，尺寸正则化参数ε中的中间极点在可观测值中消失，并且经典理论没有重新归一化。我们对一系列与我们相符的可观测数据进行了说明。