辐射阻尼与泛函微分方程
Radiative Damping and Functional Differential Equations
摘要：
提出了一种求解带辐射阻尼的经典多体问题的一般方法。我们修正了麦克斯韦电动力学的短程结构。这使我们能够避免失控的解决方案，如果我们有一个协变模型的扩展粒子。由此产生的运动方程是泛函微分方程（FDES），而不是常微分方程。使用最近开发的数值技术刚性FDES，我们解决这些方程的一个机构的中心力问题的辐射阻尼，以期基准我们的新方法。我们的结果表明，局部的辐射阻尼的大小可以很好地近似的标准的三阶表达式，但我们的解决方案的整体性质是显着不同的。评述了两体问题及其在量子场论和量子力学中的应用。
英文摘要：
We propose a general technique to solve the classical many-body problem with radiative damping. We modify the short-distance structure of Maxwell electrodynamics. This allows us to avoid runaway solutions as if we had a covariant model of extended particles. The resulting equations of motion are functional differential equations (FDEs) rather than ordinary differential equations. Using recently developed numerical techniques for stiff FDEs, we solve these equations for the one-body central force problem with radiative damping with a view to benchmark our new approach. Our results indicate that locally the magnitude of radiation damping may be well approximated by the standard third-order expression but the global properties of our solutions are dramatically different. We comment on the two body problem and applications to quantum field theory and quantum mechanics.
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