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Transformationsverhalten der Ströme und Felder Eq: math.2174.10

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TeX (original user input):

\begin{align}
& \Delta \bar{A}\left( \bar{r},t \right)-\frac{1}{{{c}^{2}}}\frac{{{\partial }^{2}}}{\partial {{t}^{2}}}\bar{A}\left( \bar{r},t \right)=-{{\mu }_{0}}\bar{j} \\
& \#\bar{A}\left( \bar{r},t \right)=-{{\mu }_{0}}\bar{j} \\
& \#=-{{\partial }_{\mu }}{{\partial }^{\mu }} \\
& {{\mu }_{0}}c=\frac{1}{{{\varepsilon }_{0}}c} \\
& \#\bar{A}\left( \bar{r},t \right)=-{{\mu }_{0}}\bar{j}\Leftrightarrow {{\partial }_{\mu }}{{\partial }^{\mu }}c{{A}^{\alpha }}=\frac{1}{{{\varepsilon }_{0}}c}{{j}^{\alpha }} \\
& \alpha =1,2,3 \\
\end{align}

TeX (checked):

{\begin{aligned}&\Delta {\bar {A}}\left({\bar {r}},t\right)-{\frac {1}{{c}^{2}}}{\frac {{\partial }^{2}}{\partial {{t}^{2}}}}{\bar {A}}\left({\bar {r}},t\right)=-{{\mu }_{0}}{\bar {j}}\\&\#{\bar {A}}\left({\bar {r}},t\right)=-{{\mu }_{0}}{\bar {j}}\\&\#=-{{\partial }_{\mu }}{{\partial }^{\mu }}\\&{{\mu }_{0}}c={\frac {1}{{{\varepsilon }_{0}}c}}\\&\#{\bar {A}}\left({\bar {r}},t\right)=-{{\mu }_{0}}{\bar {j}}\Leftrightarrow {{\partial }_{\mu }}{{\partial }^{\mu }}c{{A}^{\alpha }}={\frac {1}{{{\varepsilon }_{0}}c}}{{j}^{\alpha }}\\&\alpha =1,2,3\\\end{aligned}}

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\begin{aligned} Δ \bar{A} (\bar{r}, t) - \frac{1}{c^{2}} \frac{\partial^{2}}{\partial t^{2}} \bar{A} (\bar{r}, t) = - μ_{0} \bar{j} \\ # \bar{A} (\bar{r}, t) = - μ_{0} \bar{j} \\ # = - \partial_{μ} \partial^{μ} \\ μ_{0} c = \frac{1}{ε_{0} c} \\ # \bar{A} (\bar{r}, t) = - μ_{0} \bar{j} \Leftrightarrow \partial_{μ} \partial^{μ} c A^{α} = \frac{1}{ε_{0} c} j^{α} \\ α = 1, 2, 3 \end{aligned}

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Identifiers

$Δ$

$\bar{A}$

$\bar{r}$

$t$

$c$

$t$

$\bar{A}$

$\bar{r}$

$t$

$μ_{0}$

$\bar{j}$

$\bar{A}$

$\bar{r}$

$t$

$μ_{0}$

$\bar{j}$

$μ$

$μ$

$μ_{0}$

$c$

$ε_{0}$

$c$

$\bar{A}$

$\bar{r}$

$t$

$μ_{0}$

$\bar{j}$

$μ$

$μ$

$c$

$A$

$α$

$ε_{0}$

$c$

$j$

$α$

$α$

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