On the self-force in Bopp-Podolsky electrodynamics
On the self-force in Bopp-Podolsky electrodynamics
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论Bopp-Podolsky电动力学中的自力
DOI：
10.1088/1751-8113/48/43/435401
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Gratus J
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文献类型：
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作者：
Gratus J
在经典真空麦克斯韦-洛伦兹理论中，带电点粒子的自力是无限的。这使得经典质量重整化成为必要，并且在狭义相对论领域中，导致亚伯拉罕-洛伦兹-狄拉克运动方程拥有非物理失控和预加速解。在本文中，我们研究了 Bopp、Landé、Thomas 和 Podolsky 在 20 世纪 40 年代提出的经典真空电动力学的高阶修正是否可以解决这个问题。由于该理论是线性的，格林函数技术使人们能够将闵可夫斯基时空上的带电点粒子的场写为粒子历史的积分。通过引入“远离向后光锥”的类时世界线的概念，我们能够规定此类积分的收敛标准。我们还展示了一条类时世界线，在时空的类光超平面上产生奇异场。在这种情况下，当粒子穿过超平面时，场是轻微奇异的。即使在波普-波多尔斯基场有界的情况下，当人们接近点粒子时，它也会表现出方向不连续性。我们描述了一种为粒子世界线上的场赋值的过程，该过程使人们能够定义有限的洛伦兹自力。这是明确导出的，导致外部电磁场中粒子运动的积分微分方程。我们得出的结论是，属于本文讨论类别的该方程的任何世界线解都具有连续的四速度。
In the classical vacuum Maxwell–Lorentz theory the self-force of a charged point particle is infinite. This makes classical mass renormalization necessary and, in the special relativistic domain, leads to the Abraham–Lorentz–Dirac equation of motion possessing unphysical run-away and pre-acceleration solutions. In this paper we investigate whether the higher-order modification of classical vacuum electrodynamics suggested by Bopp, Landé, Thomas and Podolsky in the 1940s, can provide a solution to this problem. Since the theory is linear, Green-function techniques enable one to write the field of a charged point particle on Minkowski spacetime as an integral over the particle's history. By introducing the notion of timelike worldlines that are'bounded away from the backward light-cone'we are able to prescribe criteria for the convergence of such integrals. We also exhibit a timelike worldline yielding singular fields on a lightlike hyperplane in spacetime. In this case the field is mildly singular at the event where the particle crosses the hyperplane. Even in the case when the Bopp–Podolsky field is bounded, it exhibits a directional discontinuity as one approaches the point particle. We describe a procedure for assigning a value to the field on the particle worldline which enables one to define a finite Lorentz self-force. This is explicitly derived leading to an integro-differential equation for the motion of the particle in an external electromagnetic field. We conclude that any worldline solutions to this equation belonging to the categories discussed in the paper have continuous four-velocities.