关于有理电磁场
On rational electromagnetic fields
摘要：
我们采用最近开发的方法来构建合理的电磁场配置在闵可夫斯基空间调查这些无源有限作用麦克斯韦（“结”）解决方案的几个属性。该结构发生在彭罗斯图上，但使用了德西特空间的特征，特别是它的等距群。这承认一个分类的所有纽结解决方案的$S^3$谐波，标记为自旋$2j\in{\mathbb N}_0$，这实际上提供了一个完整的"结基础"的有限作用麦克斯韦场。给出了一个$j{=}1$的例子，计算了任意自旋-$j$组态的能量，导出了自旋与螺旋度之间的线性关系，并刻画了零场的子空间.最后，我们提出了零无穷远处的电磁通量的表达式，并证明了它与总能量相等。
英文摘要：
We employ a recently developed method for constructing rational electromagnetic field configurations in Minkowski space to investigate several properties of these source-free finite-action Maxwell ("knot") solutions. The construction takes place on the Penrose diagram but uses features of de Sitter space, in particular its isometry group. This admits a classification of all knot solutions in terms of $S^3$ harmonics, labelled by a spin $2j\in{\mathbb N}_0$, which in fact provides a complete "knot basis" of finite-action Maxwell fields. We display a $j{=}1$ example, compute the energy for arbitrary spin-$j$ configurations, derive a linear relation between spin and helicity and characterize the subspace of null fields. Finally, we present an expression for the electromagnetic flux at null infinity and demonstrate its equality with the total energy.
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