中立时滞与电动力学的推广
Neutral Delay and a Generalization of Electrodynamics
摘要：
电磁二体问题的方程是中性时滞方程，对于一般的初始数据，其解具有不连续的导数。如果要使用这些中立型时滞方程与任意的初始数据，解决方案与不连续的衍生物必须是允许的。令人惊讶的是，同样的中性是兼容的最近开发的变分方法与混合型边界的惠勒-费曼电动力学。我们表明，两体电磁轨道与不连续的速度是物理上必要的，表明消失的远场几乎无处不在的轨道必须有一些不连续的速度在几个点上。我们推广的惠勒-费曼电动力学与变分方法，包括所有连续的轨迹，允许分段可微的弱解的轨迹定义几乎无处不在（但在一组点的零测量速度跳）。随着这一推广，我们制定了广义吸收体假设，远场渐近消失几乎无处不在，并表明满足广义吸收体假设的有界两体轨道需要有几个点上的不连续导数。我们也给出了有界非辐射二体轨道族的一般解。我们讨论的物理轨道与不连续的衍生物，并表明，这些保存的物理动量，强调经典变分方法的差异。最后，讨论了混合型边界电磁变分法是适定的但缺乏可逆性的问题。
英文摘要：
The equations for the electromagnetic two-body problem are neutral-delay equations that for generic initial data have solutions with discontinuous derivatives. If one wants to use these neutral-delay equations with arbitrary initial data, solutions with discontinuous derivatives must be allowed. Surprisingly, this same neutrality is compatible with the recently developed variational method with mixed-type boundaries for the Wheeler-Feynman electrodynamics. We show that two-body electromagnetic orbits with discontinuous velocities are physically necessary by showing that orbits with vanishing far-fields amost everywhere must have some discontinuous velocities on a few points. We generalize the Wheeler-Feynman electrodynamics with the variational method to include all continuous trajectories, allowing piecewise-differentiable weak solutions represented by trajectories with fields defined almost everywhere (but on a set of points of zero measure where velocities jump). Along with this generalization we formulate the generalized absorber hypothesis that the far-fields vanish asymptotically almost everywhere and show that bounded two-body orbits satisfying the generalized absorber hypothesis need to have discontinuous derivatives on a few points. We also give the general solution for the family of bounded non-radiating two-body orbits. We discuss the physics of orbits with discontinuous derivatives and show that these conserve the physical momentum, stressing the differences to classical variational methods. Last, we discuss how the electromagnetic variational method with mixed-type boundaries is well-posed but lacks reversibilty.
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。
