arXiv 1109.22642011-09hep-th

三维时空中磁事件场中的电荷

Electric charge in the field of a magnetic event in three-dimensional spacetime

Claudio Bunster, Cristian Martinez

备注：: Version to appear in Phys. Rev. D
DOI：: 10.1103/PhysRevD.85.045024

摘要：

我们分析了三维时空中磁荷事件场中电荷的运动。我们首先展示运动方程的第一个积分的时空角动量的三个守恒分量，然后进行数值计算。在穿过事件的光锥之后，最初处于静止状态的电荷开始旋转并减速。问题中出现了两个长度：（i）特征长度$\frac{q g}{2 πm}$，其中$q$和$m$是粒子的电荷和质量，$g$是事件的磁荷;（ii）时空碰撞参数$r_0$。对$r_0 \gg \frac{q g}{2 πm}$来说，经过一个有序时间$r_0$后，粒子急剧地转了四分之一圈，停在过去事件发生的同一个空间位置。这种跳跃是由电荷感觉到的磁事件存在的主要标志。附录中给出了在磁表示中使用诺特定理的角动量表达式的推导。

英文摘要：

We analyze the motion of an electric charge in the field of a magnetically charged event in three-dimensional spacetime. We start by exhibiting a first integral of the equations of motion in terms of the three conserved components of the spacetime angular momentum, and then proceed numerically. After crossing the light cone of the event, an electric charge initially at rest starts rotating and slowing down. There are two lengths appearing in the problem: (i) the characteristic length $\frac{q g}{2 πm}$, where $q$ and $m$ are the electric charge and mass of the particle, and $g$ is the magnetic charge of the event; and (ii) the spacetime impact parameter $r_0$. For $r_0 \gg \frac{q g}{2 πm}$, after a time of order $r_0$, the particle makes sharply a quarter of a turn and comes to rest at the same spatial position at which the event happened in the past. This jump is the main signature of the presence of the magnetic event as felt by an electric charge. A derivation of the expression for the angular momentum that uses Noether's theorem in the magnetic representation is given in the Appendix.

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