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Display information for equation id:math.1199.1241 on revision:1199

* Page found: Elektrodynamik Schöll (eq math.1199.1241)

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Transformationsverhalten der Ströme und Felder Eq: math.2174.51

Hash: a293efff8d86199659669f099a081c4a

TeX (original user input):

\begin{align}
& {{\varepsilon }^{\kappa \lambda \mu \nu }}\acute{\ }={{U}^{\kappa }}_{\alpha }{{U}^{\lambda }}_{\beta }{{U}^{\mu }}_{\gamma }{{U}^{\nu }}_{\delta }{{\varepsilon }^{\alpha \beta \gamma \delta }} \\
& =\left| \begin{matrix}
{{U}^{\kappa }}_{0} & {{U}^{\kappa }}_{1} & {{U}^{\kappa }}_{2} & {{U}^{\kappa }}_{3}  \\
{{U}^{\lambda }}_{0} & {{U}^{\lambda }}_{1} & {{U}^{\lambda }}_{2} & {{U}^{\lambda }}_{3}  \\
{{U}^{\mu }}_{0} & {{U}^{\mu }}_{1} & {{U}^{\mu }}_{2} & {{U}^{\mu }}_{3}  \\
{{U}^{\nu }}_{0} & {{U}^{\nu }}_{1} & {{U}^{\nu }}_{2} & {{U}^{\nu }}_{3}  \\
\end{matrix} \right|=\left( \det U \right)\cdot {{\varepsilon }^{\kappa \lambda \mu \nu }} \\
& \left( \det U \right)=\pm 1 \\
\end{align}

TeX (checked):

{\begin{aligned}&{{\varepsilon }^{\kappa \lambda \mu \nu }}{\acute {\ }}={{U}^{\kappa }}_{\alpha }{{U}^{\lambda }}_{\beta }{{U}^{\mu }}_{\gamma }{{U}^{\nu }}_{\delta }{{\varepsilon }^{\alpha \beta \gamma \delta }}\\&=\left|{\begin{matrix}{{U}^{\kappa }}_{0}&{{U}^{\kappa }}_{1}&{{U}^{\kappa }}_{2}&{{U}^{\kappa }}_{3}\\{{U}^{\lambda }}_{0}&{{U}^{\lambda }}_{1}&{{U}^{\lambda }}_{2}&{{U}^{\lambda }}_{3}\\{{U}^{\mu }}_{0}&{{U}^{\mu }}_{1}&{{U}^{\mu }}_{2}&{{U}^{\mu }}_{3}\\{{U}^{\nu }}_{0}&{{U}^{\nu }}_{1}&{{U}^{\nu }}_{2}&{{U}^{\nu }}_{3}\\\end{matrix}}\right|=\left(\det U\right)\cdot {{\varepsilon }^{\kappa \lambda \mu \nu }}\\&\left(\det U\right)=\pm 1\\\end{aligned}}

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\begin{aligned} ε^{κ λ μ ν} \overset{´}{} = {U^{κ}}_{α} {U^{λ}}_{β} {U^{μ}}_{γ} {U^{ν}}_{δ} ε^{α β γ δ} \\ = | \begin{matrix} {U^{κ}}_{0} & {U^{κ}}_{1} & {U^{κ}}_{2} & {U^{κ}}_{3} \\ {U^{λ}}_{0} & {U^{λ}}_{1} & {U^{λ}}_{2} & {U^{λ}}_{3} \\ {U^{μ}}_{0} & {U^{μ}}_{1} & {U^{μ}}_{2} & {U^{μ}}_{3} \\ {U^{ν}}_{0} & {U^{ν}}_{1} & {U^{ν}}_{2} & {U^{ν}}_{3} \end{matrix} | = (\det U) \cdot ε^{κ λ μ ν} \\ (\det U) = \pm 1 \end{aligned}

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$\overset{´}{}$

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