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Display information for equation id:math.1107.223 on revision:1107

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TeX (original user input):

\left. \begin{align}
  & {{F}^{\mu \nu }}_{,\nu }=\frac{4\pi }{c}{{j}^{\mu }} \\ 
 & {{\varepsilon }^{\nu \mu \alpha \beta }}{{F}_{\alpha \beta ,\mu }}=0  
\end{align} \right\}\to \left\{ \begin{align}
  & {{F}^{\mu \nu }}_{;\nu }=\frac{4\pi }{c}{{j}^{\mu }} \\ 
 & \frac{1}{\sqrt{-g}}{{\varepsilon }^{\nu \mu \alpha \beta }}{{F}_{\alpha \beta ;\mu }}=0  
\end{align} \right.\Leftrightarrow \left\{ \begin{align}
  & \frac{1}{\sqrt{-g}}{{\left( \sqrt{-g}{{F}^{\mu \nu }} \right)}_{,\nu }}=\frac{4\pi }{c}{{j}^{\mu }} \\ 
 & {{\varepsilon }^{\nu \mu \alpha \beta }}{{F}_{\alpha \beta ,\mu }}=0  
\end{align} \right.

TeX (checked):

\left.{\begin{aligned}&{{F}^{\mu \nu }}_{,\nu }={\frac {4\pi }{c}}{{j}^{\mu }}\\&{{\varepsilon }^{\nu \mu \alpha \beta }}{{F}_{\alpha \beta ,\mu }}=0\end{aligned}}\right\}\to \left\{{\begin{aligned}&{{F}^{\mu \nu }}_{;\nu }={\frac {4\pi }{c}}{{j}^{\mu }}\\&{\frac {1}{\sqrt {-g}}}{{\varepsilon }^{\nu \mu \alpha \beta }}{{F}_{\alpha \beta ;\mu }}=0\end{aligned}}\right.\Leftrightarrow \left\{{\begin{aligned}&{\frac {1}{\sqrt {-g}}}{{\left({\sqrt {-g}}{{F}^{\mu \nu }}\right)}_{,\nu }}={\frac {4\pi }{c}}{{j}^{\mu }}\\&{{\varepsilon }^{\nu \mu \alpha \beta }}{{F}_{\alpha \beta ,\mu }}=0\end{aligned}}\right.

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MathML (4.791 KB / 554 B) :

\begin{aligned} {F^{μ ν}}_{, ν} = \frac{4 π}{c} j^{μ} \\ ε^{ν μ α β} F_{α β, μ} = 0 \end{aligned}} \to {\begin{aligned} {F^{μ ν}}_{; ν} = \frac{4 π}{c} j^{μ} \\ \frac{1}{\sqrt{- g}} ε^{ν μ α β} F_{α β; μ} = 0 \end{aligned} \Leftrightarrow {\begin{aligned} \frac{1}{\sqrt{- g}} {(\sqrt{- g} F^{μ ν})}_{, ν} = \frac{4 π}{c} j^{μ} \\ ε^{ν μ α β} F_{α β, μ} = 0 \end{aligned}

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Identifiers

$F$

$μ$

$ν$

$ν$

$π$

$c$

$j$

$μ$

$ε$

$ν$

$μ$

$α$

$β$

$F_{α β, μ}$

$F$

$μ$

$ν$

$ν$

$π$

$c$

$j$

$μ$

$g$

$ε$

$ν$

$μ$

$α$

$β$

$F$

$α$

$β$

$μ$

$g$

$g$

$F$

$μ$

$ν$

$ν$

$π$

$c$

$j$

$μ$

$ε$

$ν$

$μ$

$α$

$β$

$F_{α β, μ}$

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