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Display information for equation id:math.1109.107 on revision:1109

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TeX (original user input):

\begin{align}
  & d{{s}^{2}}={{\eta }_{\mu \nu }}\partial {{'}_{\alpha }}{{x}^{\mu }}\partial {{'}_{\beta }}{{x}^{\nu }}dx{{'}^{\alpha }}dx{{'}^{\beta }} \\ 
 & =\left[ {{c}^{2}}-{{\omega }^{2}}\left( {{\left( x{{'}^{1}} \right)}^{2}}+{{\left( x{{'}^{2}} \right)}^{2}} \right) \right]dt{{'}^{2}}+2\omega x{{'}^{2}}dx{{'}^{1}}dt'-2\omega x{{'}^{1}}dx{{'}^{2}}dt'-{{\left( dx{{'}^{2}} \right)}^{2}}-{{\left( dx{{'}^{3}} \right)}^{2}}  
\end{align}

TeX (checked):

{\begin{aligned}&d{{s}^{2}}={{\eta }_{\mu \nu }}\partial {{'}_{\alpha }}{{x}^{\mu }}\partial {{'}_{\beta }}{{x}^{\nu }}dx{{'}^{\alpha }}dx{{'}^{\beta }}\\&=\left[{{c}^{2}}-{{\omega }^{2}}\left({{\left(x{{'}^{1}}\right)}^{2}}+{{\left(x{{'}^{2}}\right)}^{2}}\right)\right]dt{{'}^{2}}+2\omega x{{'}^{2}}dx{{'}^{1}}dt'-2\omega x{{'}^{1}}dx{{'}^{2}}dt'-{{\left(dx{{'}^{2}}\right)}^{2}}-{{\left(dx{{'}^{3}}\right)}^{2}}\end{aligned}}

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MathML (3.224 KB / 499 B) :

\begin{aligned} d s^{2} = η_{μ ν} \partial'_{α} x^{μ} \partial'_{β} x^{ν} d x'^{α} d x'^{β} \\ = [c^{2} - ω^{2} ({(x'^{1})}^{2} + {(x'^{2})}^{2})] d t'^{2} + 2 ω x'^{2} d x'^{1} d t^{'} - 2 ω x'^{1} d x'^{2} d t^{'} - {(d x'^{2})}^{2} - {(d x'^{3})}^{2} \end{aligned}

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$d$

$s$

$η_{μ ν}$

$α$

$x$

$μ$

$β$

$x$

$ν$

$d$

$x$

$α$

$d$

$x$

$β$

$c$

$ω$

$x$

$x$

$d$

$t$

$ω$

$x$

$d$

$x$

$d$

$t$

$ω$

$x$

$d$

$x$

$d$

$t$

$d$

$x$

$d$

$x$

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