论文标题
在理性电磁场上
On rational electromagnetic fields
论文作者
论文摘要
我们采用了一种最近开发的方法来构建Minkowski空间中的有理电磁场配置，以研究这些无源有限的麦克斯韦（“调子”）解决方案的几种特性。该结构发生在Penrose图上，但使用了De Sitter空间的特征，尤其是其等距组。这在{\ mathbb n} _0 $中以$ s^3 $谐波表示对所有结解决方案的分类，实际上提供了有限的麦克斯韦字段的完整“结”。我们显示一个$ j {=} 1 $示例，计算任意自旋的能量 - $ J $配置，得出旋转和螺旋性之间的线性关系，并表征无效字段的子空间。最后，我们提出了无限无穷大的电磁通量的表达，并证明了其与总能量的平等性。
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.
