论文标题
赫兹形式的相对论起源，并扩展了麦克斯韦电磁理论的赫兹形式方程
Relativistic origin of Hertz-form and extended Hertz-form equations for Maxwell theory of electromagnetism
论文作者
论文摘要
我们明确地表明，赫兹形式的麦克斯韦方程及其扩展可以从麦克斯韦方程的洛伦兹转换的非相关主义扩展中获得。扩展的Hertz形式方程中参数$α$的显式表达式可以从这种非相关主义扩展中得出。扩展的Hertz形式方程不保留Galilean的不变性，来自Lorentz的Maxwell方程转换，与Galilean Transformed Maxwell方程（原始HERTZ方程）不同，其相对符号的相对符号差异。 D'Alembert方程从扩展的HERTZ形式方程式所说明的超亮度行为应通过在$ v/c $扩展中包括所有转向的贡献来删除，尽管由于$α= 0 $，因此不会在真空中出现这种超亮度行为。我们应该注意，以赫兹形式并扩展了赫兹形式方程，电磁字段应采用表格$ \ vec {\ mathcal {e}}}}（x）= \ vec {e}（λ^{ - 1} x）$和$ \ vec {\ Mathcal {b}}（x）= \ vec {b}（λ^{ - 1} x）$。这种对字段的描述选择与$ \ vec {e}（x）$和$ \ vec {b}（x）$不同，这是众所周知的，可以满足普通的麦克斯韦方程。使用功能集$ \ {\ vec {\ Mathcal {e}}（x）（x），\ vec {\ Mathcal {b}}（x）\} $的描述电磁现象的描述$ \ {\ vec {\ Mathcal {e}}（x），\ vec {\ Mathcal {b}}}}（x）\} $描述在低速近似中满足扩展的Hertz-form Maxwell的方程。 （扩展）Hertz形式的麦克斯韦方程的解描述了行动波形的电磁场。
We show explicitly that the Hertz-form Maxwell's equations and their extensions can be obtained from the non-relativistic expansion of Lorentz transformation of Maxwell's equations. The explicit expression for the parameter $α$ in the extended Hertz-form equations can be derived from such a non-relativistic expansion. The extended Hertz-form equations, which do not preserve Galilean invariance, origin from Lorentz transformation of Maxwell's equations and differ from the Galilean-transformed Maxwell equations (the original Hertz equations) by the relative sign differences between the two $α$ terms etc. Especially, the $α$ parameter is of relativistic origin. The superluminal behavior illustrated by the D'Alembert equation from the extended Hertz-form equations should be removed by including all subleading contributions in the $v/c$ expansion, although such a superluminal behavior will not occur in the vacuum because $α=0$. We should note that in the Hertz form and extended Hertz form equations, the electromagnetic fields should take the forms $ \vec{\mathcal{E}}(x)=\vec{E}(Λ^{-1}x)$ and $ \vec{\mathcal{B}}(x)=\vec{B}(Λ^{-1}x)$. Such a choice of description for the fields is different from the ordinary one with $\vec{E}(x)$ and $\vec{B}(x)$, which are well known to satisfy the ordinary Maxwell's equations. The descriptions of electromagnetic phenomena using the function set $\{\vec{\mathcal{E}}(x),\vec{\mathcal{B}}(x)\}$ and the function set $(\vec{E}(x),\vec{B}(x))$ are equivalent, with the $\{\vec{\mathcal{E}}(x),\vec{\mathcal{B}}(x)\}$ description satisfying the extended Hertz-form Maxwell's equations in the low speed approximation. The solution of (extended) Hertz-form Maxwell's equations describe the traveling wave form electromagnetic field.
