We construct a new Yang-Mills Lagrangian based on a notion of minimal coupling that incorporates classical spin effects. The construction relies on the introduction of a new covariant derivative, which we name “classical spin covariant derivative”, that is compatible with the three-point interaction of the \( \sqrt{\textrm{Kerr}} \) solution with the gauge field. The resulting Lagrangian, besides the correct three-point coupling, predicts a unique choice for contact terms and therefore it can be used to compute higher-point amplitudes such as the Compton, unaffected by spurious poles. Using double copy techniques we use this theory to extract gravity amplitudes and observables that are relevant to describe Kerr binary dynamics to all orders in the spin. In particular, we compute the 2PM (\( \mathcal{O} \)(\( {G}_N^2 \))) 2 → 2 elastic scattering amplitude between two classically spinning objects to all orders in the spin and use it to extract the 2PM scattering angle.

我们基于最小耦合概念并结合了经典自旋效应构建了一个新的杨-米尔斯拉格朗日量。该构造依赖于引入一种新的协变导数，我们将其命名为“经典自旋协变导数”，它与\( \sqrt{\textrm{Kerr}} \)解与规范的三点相互作用兼容场地。由此产生的拉格朗日，除了正确的三点耦合之外，还预测了接触项的独特选择，因此它可以用于计算更高点的振幅，例如康普顿，而不受杂散极点的影响。使用双复制技术，我们使用该理论来提取与描述自旋中所有阶的克尔二元动力学相关的重力振幅和可观测量。特别是，我们计算两个经典旋转物体之间所有阶次的2PM ( \( \mathcal{O} \) ( \( {G}_N^2 \) )) 2 → 2 弹性散射振幅并使用它提取 2PM 散射角。