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Transformationsverhalten der Ströme und Felder Eq: math.2174.34

Hash: 837ff81445011e80e01ad2beaa42199f

TeX (original user input):

\begin{align}
& E{{\acute{\ }}^{1}}=F{{\acute{\ }}^{10}}={{U}^{1}}_{\lambda }{{U}^{0}}_{\kappa }{{F}^{\lambda \kappa }}=-\beta \gamma {{U}^{0}}_{\kappa }{{F}^{0\kappa }}+\gamma {{U}^{0}}_{\kappa }{{F}^{1\kappa }}={{\left( \beta \gamma  \right)}^{2}}{{F}^{01}}+{{\gamma }^{2}}{{F}^{10}}= \\
& ={{\gamma }^{2}}\left( 1-{{\beta }^{2}} \right){{F}^{10}}={{E}^{1}} \\
& {{\gamma }^{2}}\left( 1-{{\beta }^{2}} \right)=1 \\
&  \\
& E{{\acute{\ }}^{2}}=F{{\acute{\ }}^{20}}={{U}^{2}}_{\lambda }{{U}^{0}}_{\kappa }{{F}^{\lambda \kappa }}={{U}^{0}}_{\kappa }{{F}^{2\kappa }}=\gamma {{F}^{20}}-\beta \gamma {{F}^{21}}=\gamma \left( {{E}^{2}}-v{{B}^{3}} \right) \\
\end{align}

TeX (checked):

{\begin{aligned}&E{{\acute {\ }}^{1}}=F{{\acute {\ }}^{10}}={{U}^{1}}_{\lambda }{{U}^{0}}_{\kappa }{{F}^{\lambda \kappa }}=-\beta \gamma {{U}^{0}}_{\kappa }{{F}^{0\kappa }}+\gamma {{U}^{0}}_{\kappa }{{F}^{1\kappa }}={{\left(\beta \gamma \right)}^{2}}{{F}^{01}}+{{\gamma }^{2}}{{F}^{10}}=\\&={{\gamma }^{2}}\left(1-{{\beta }^{2}}\right){{F}^{10}}={{E}^{1}}\\&{{\gamma }^{2}}\left(1-{{\beta }^{2}}\right)=1\\&\\&E{{\acute {\ }}^{2}}=F{{\acute {\ }}^{20}}={{U}^{2}}_{\lambda }{{U}^{0}}_{\kappa }{{F}^{\lambda \kappa }}={{U}^{0}}_{\kappa }{{F}^{2\kappa }}=\gamma {{F}^{20}}-\beta \gamma {{F}^{21}}=\gamma \left({{E}^{2}}-v{{B}^{3}}\right)\\\end{aligned}}

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\begin{aligned} E {\overset{´}{}}^{1} = F {\overset{´}{}}^{10} = {U^{1}}_{λ} {U^{0}}_{κ} F^{λ κ} = - β γ {U^{0}}_{κ} F^{0 κ} + γ {U^{0}}_{κ} F^{1 κ} = {(β γ)}^{2} F^{01} + γ^{2} F^{10} = \\ = γ^{2} (1 - β^{2}) F^{10} = E^{1} \\ γ^{2} (1 - β^{2}) = 1 \\ E {\overset{´}{}}^{2} = F {\overset{´}{}}^{20} = {U^{2}}_{λ} {U^{0}}_{κ} F^{λ κ} = {U^{0}}_{κ} F^{2 κ} = γ F^{20} - β γ F^{21} = γ (E^{2} - v B^{3}) \end{aligned}

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Identifiers

$E$

$\overset{´}{}$

$F$

$\overset{´}{}$

$U_{λ}$

$U_{κ}$

$F$

$λ$

$κ$

$β$

$γ$

$U_{κ}$

$F$

$κ$

$γ$

$U_{κ}$

$F$

$κ$

$β$

$γ$

$F$

$γ$

$F$

$γ$

$β$

$F$

$E$

$γ$

$β$

$E$

$\overset{´}{}$

$F$

$\overset{´}{}$

$U_{λ}$

$U_{κ}$

$F$

$λ$

$κ$

$U_{κ}$

$F$

$κ$

$γ$

$F$

$β$

$γ$

$F$

$γ$

$E$

$v$

$B$

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