主导反常、漂移哈密顿量和相对论二体系统
Leading anomalies, the drift Hamiltonian and the relativistic two-body system
摘要：
我们建议解决运动的两个身体的问题，在广义相对论通过确定领先的违反守恒量，被称为（相对论）异常，有序的后牛顿秩序，他们出现。这不同于在规定的顺序内获得完整解决方案的标准程序。我们发现，描述守恒量空间中漂移的约化哈密顿量是由微扰哈密顿量的平均值给出的。使用这种方法，在推导时间演化之前进行平均，从而节省了计算。计算变得类似于那些在汉密尔顿-雅可比方法，而留在更舒适的设置的哈密顿公式。我们应用这种方法的领先的异常和漂移哈密顿的二元问题，并处理几个扰动：1 PN，自旋轨道和自旋自旋。在此过程中，我们讨论了拉普拉斯-龙格-伦茨向量作为动量空间中保标度共形变换的生成元的解释。
英文摘要：
We suggest to solve for the motion of the two body problem in General Relativity by identifying the leading violation of conserved quantities, referred to as (relativistic) anomalies, ordered by the post-Newtonian order at which they appear. This differs from the standard procedure of obtaining the full solution up to a prescribed order. We find that the reduced Hamiltonian which describes the drift in the space of conserved quantities is given by the average of the perturbation Hamiltonian. Using this approach the averaging is done prior to the derivation of time evolution, thereby economizing the computation. The computations become similar to those in the Hamilton-Jacobi method, while staying in the more comfortable setting of the Hamiltonian formulation. We apply this approach of leading anomalies and the drift Hamiltonian to the binary problem and treat several perturbations: 1PN, spin-orbit and spin-spin. On the way we discuss the interpretation of the Laplace-Runge-Lenz vector as a generator of scale-preserving conformal transformations in momentum space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
