自作用力问题的统一处理
A Unified Treatment of the Self-Force Problem
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中文总结 AI 辅助
本文基于世界线有效场论提出普适形式体系，用闭时间路径积分推导有效作用量，可相对论性计算引力自作用力，验证了库仑对数的普适性，完善了自作用力问题的统一处理。
中文摘要 AI 辅助
本文提出了一种基于世界线有效场论的形式体系，该体系可系统计算浸没在非零应力能量环境中的致密天体所受的引力自作用力。利用闭时间路径积分，我们给出了一种普适有效作用量，可用于计算致密天体因与环境相互作用产生的运动方程，其精度可达相关展开参数的任意阶，而展开参数的相对重要性取决于环境的选择。我们证明，领头阶运动方程可普遍地用环境的应力能量张量推迟两点函数表示。所得作用量可完全相对论性地计算耗散力（动力学摩擦）和保守力。我们通过计算尘埃、无粘流体和相干场产生的耗散力，验证了该结果的实用性，所得结果与现有文献中的推导一致。我们还证明，钱德拉塞卡发现的著名“库仑对数”应被解释为重整化群对数，源于对in-in作用量耗散部分进行重整化的紫外发散。随后我们证明，在牛顿极限下，该对数对一类通用的环境和轨道而言具有普适性，其数值是普适的。该对数是耗散作用量中尚未被探索的重整化群流的领头对数。
英文摘要
This paper introduces formalism, based on worldline effective field theory, which allows one to systematically calculate the gravitational self-force on a compact object immersed in an environment with non-vanishing stress energy. Using the closed time path integral we present a universal effective action that can be used to calculate the equations of motion of a compact object due to its interaction with the environment to any order in the relevant expansion parameters, the relative importance of which depends upon the choice of environment. We show that the leading order equations of motion can be universally written in terms of the retarded two-point function of the stress-energy tensor for the environment. The resulting action can be used to calculate both dissipative (dynamical friction) and conservative forces in a completely relativistic fashion. We demonstrate the utility of the result by calculating the dissipative force due to dust, an inviscid fluid, and a coherent field. Our results agree with those previously derived in the literature. We furthermore show that the famous ``Coulomb Log" found by Chandrasekhar should be interpreted as a renormalization group log due to a UV divergence that renormalizes the dissipative part of the in-in action. We then prove that this log is universal in the Newtonian limit in that its value is universal, for a generic class of environments and trajectories. This log is the leading log in an RG flow in the dissipative action that has yet to be explored.
发表机构
- Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）
- Carnegie Mellon University（卡内基梅隆大学）
机构由 AI 辅助整理，请以论文原文为准。
