论文标题
对固定质量矢量和对称张量场的多极分析
Multipole analysis on stationary massive vector and symmetric tensor fields
论文作者
论文摘要
通过使用不可减至的笛卡尔张量来获得空间紧凑的固定源外部区域中大规模矢量和对称张量场的多极扩展，并提供了用于源多极矩的封闭形式表达式。这些膨胀显示了类似Yukawa的依赖性对磁场的大量参数，并且固定源多极矩的积分都由与源分布相关的常见径向因子调节。对于固定的巨大矢量场，有两种类型的``磁''多极矩，其中一个是磁静态场的概括，另一种是固定质量巨型矢量场的另一组多极矩，无法转换。至于固定的巨大对称张量场，当指定其空间部分的痕迹时，会出现其多极膨胀，除了质量和无质量对称张量张力场的质量和自旋多极矩外，还出现了三组多个多极矩。讨论了两个典型情况下张量场的多极膨胀，在这里表明，如果张量场的空间部分无迹线，则相应膨胀中的单极和偶极矩将消失。
The multipole expansions for massive vector and symmetric tensor fields in the region outside spatially compact stationary sources are obtained by using the symmetric and trace-free formalism in terms of the irreducible Cartesian tensors, and the closed-form expressions for the source multipole moments are provided. The expansions show a Yukawa-like dependence on the massive parameters of the fields, and the integrals of the stationary source multipole moments are all modulated by a common radial factor related to the source distribution. For stationary massive vector field, there are two types of ``magnetic'' multipole moments, among which one is the generalization of that of the magnetostatic field, and another, being an additional set of multipole moments of the stationary massive vector field, can not be transformed away. As to the stationary massive symmetric tensor field, its multipole expansion is presented when the trace of its spatial part is specified, where besides the counterparts of the mass and spin multipole moments of massless symmetric tensor field, three additional sets of multipole moments also appear. The multipole expansions of the tensor field under two typical cases are discussed, where it is shown that if the spatial part of the tensor field is trace-free, the monopole and dipole moments in the corresponding expansion will vanish.
