三维Lorentz-Dirac方程的相对论积分-微分形式
Relativistic integro-differential form of the Lorentz-Dirac equation in 3D without runaways
摘要：
众所周知，三阶洛伦兹-狄拉克方程允许失控的解决方案，其中粒子的能量增长没有限制，即使没有外力。这些解决方案可以简单地根据物理基础，并在仔细分析经典理论和量子理论之间的对应关系的基础上被否定。尽管如此，人们还是更喜欢一个一开始就不承认非物质行为的方程。这样的一个方程--洛伦兹-狄拉克方程的积分-微分版本--目前只能在一维中得到，或者只能在非相对论极限的三维中得到。本文示出了如何在没有近似的情况下对洛伦兹-狄拉克方程进行积分，从而将其转换为满足上述要求的3D中的二阶积分微分方程。即，结果，由于本质上不存在失控解，因此不需要对解进行额外的约束。推导是放置在历史背景下建立的标准工程经典电动力学的Rohrlich，和杰克逊。
英文摘要：
It is well known that the third-order Lorentz-Dirac equation admits runaway solutions wherein the energy of the particle grows without limit, even when there is no external force. These solutions can be denied simply on physical grounds, and on the basis of careful analysis of the correspondence between classical and quantum theory. Nonetheless, one would prefer an equation that did not admit unphysical behavior at the outset. Such an equation - an integro-differential version of the Lorentz-Dirac equation - is currently available either in 1 dimension only, or in 3 dimensions only in the non-relativistic limit. It is shown herein how the Lorentz-Dirac equation may be integrated without approximation, and is thereby converted to a second-order integro-differential equation in 3D satisfying the above requirement. I.E., as a result, no additional constraints on the solutions are required because runaway solutions are intrinsically absent. The derivation is placed within the historical context established by standard works on classical electrodynamics by Rohrlich, and by Jackson.
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