电磁学中的对称性提升
Symmetry Promotion in Electromagnetism
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中文总结 AI 辅助
本文研究电磁场中源分布的离散对称性在特定条件下提升为连续对称性的现象，给出仿射线性与不可约作用的条件，并通过实例展示其教学价值。
中文摘要 AI 辅助
电荷或电流的对称分布通常产生具有相同对称群的电磁场。然而，我们证明在特殊情况下，源分布的离散对称性会导致在受限区域中产生的场具有更大的连续对称性。这种从离散对称性提升到连续对称性的条件是：场必须是仿射线性的，并且源分布的对称性在环境空间上不可约地作用。我们用许多例子说明了这一效应。这一现象在教学上很有意义，既可作为静电学和静磁学中的灵感来源，也可作为群表示理论的一个易于理解的实例。
英文摘要
A symmetric distribution of charges or currents typically produces an electromagnetic field having the same symmetry group. However, under special circumstances we show that a discrete symmetry of the source distribution leads to a larger continuous symmetry for the resulting field in restricted regions. The conditions for this promotion from discrete to continuous symmetry are that the fields be affine linear and the symmetry of the source distribution act irreducibly on the ambient space. We illustrate this effect with many examples. This phenomenon is pedagogically interesting both as a source of inspiration in electro- and magnetostatics and as an accessible example of group representation theory.
发表机构
- Stanford University（斯坦福大学）
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