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Display information for equation id:math.2174.20 on revision:2174

* Page found: Transformationsverhalten der Ströme und Felder (eq math.2174.20)

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TeX (original user input): 

\begin{align}
& \tilde{\bar{A}}=\bar{A}+\nabla F \\
& \tilde{\phi }=\phi -\frac{\partial }{\partial t}F \\
& \Leftrightarrow  \\
& c{{{\tilde{A}}}^{\alpha }}=c{{A}^{\alpha }}+{{\partial }_{\alpha }}cF=c{{A}^{\alpha }}-{{\partial }^{\alpha }}cF \\
& {{{\tilde{\Phi }}}^{0}}={{\Phi }^{0}}-{{\partial }_{0}}cF={{\Phi }^{0}}-{{\partial }^{0}}cF \\
\end{align}

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A ¯ ~ = A ¯ + ∇ ⁡ F ϕ ~ = ϕ - ∂ ∂ ⁡ t ⁢ F ⇔ c ⁢ A ~ α = c ⁢ A α + ∂ α ⁡ c ⁢ F = c ⁢ A α - ∂ α ⁡ c ⁢ F Φ ~ 0 = Φ 0 - ∂ 0 ⁡ c ⁢ F = Φ 0 - ∂ 0 ⁡ c ⁢ F missing-subexpression ~ ¯ 𝐴 ¯ 𝐴 ∇ 𝐹 missing-subexpression ~ italic-ϕ italic-ϕ 𝑡 𝐹 missing-subexpression ⇔ missing-subexpression 𝑐 superscript ~ 𝐴 𝛼 𝑐 superscript 𝐴 𝛼 subscript 𝛼 𝑐 𝐹 𝑐 superscript 𝐴 𝛼 superscript 𝛼 𝑐 𝐹 missing-subexpression superscript ~ Φ 0 superscript Φ 0 subscript 0 𝑐 𝐹 superscript Φ 0 superscript 0 𝑐 𝐹 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\tilde{\bar{A}}=\bar% {A}+\nabla F\\ &\displaystyle\tilde{\phi}=\phi-\frac{\partial}{\partial t}F\\ &\displaystyle\Leftrightarrow\\ &\displaystyle c{{{\tilde{A}}}^{\alpha}}=c{{A}^{\alpha}}+{{\partial}_{\alpha}}% cF=c{{A}^{\alpha}}-{{\partial}^{\alpha}}cF\\ &\displaystyle{{{\tilde{\Phi}}}^{0}}={{\Phi}^{0}}-{{\partial}_{0}}cF={{\Phi}^{% 0}}-{{\partial}^{0}}cF\\ \end{aligned}}}

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A¯~=A¯+∇Fϕ~=ϕ−∂∂tF⇔cA~α=cAα+∂αcF=cAα−∂αcFΦ~0=Φ0−∂0cF=Φ0−∂0cF

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