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Display information for equation id:math.1446.69 on revision:1446
* Page found: Relativistische Formulierung der Elektrodynamik (eq math.1446.69)
(force rerendering)Occurrences on the following pages:
Hash: 20b398cf512f9ad511f29bc8870c0e88
TeX (original user input):
\begin{align}
& {{{\tilde{F}}}^{\mu \nu }}={{\partial }^{\mu }}{{{\tilde{\Phi }}}^{\nu }}-{{\partial }^{\nu }}{{{\tilde{\Phi }}}^{\mu }}={{\partial }^{\mu }}\left( {{\Phi }^{\nu }}+{{\partial }^{\nu }}\phi \right)-{{\partial }^{\nu }}\left( {{\Phi }^{\mu }}+{{\partial }^{\mu }}\phi \right) \\
& ={{\partial }^{\mu }}{{\Phi }^{\nu }}-{{\partial }^{\nu }}{{\Phi }^{\mu }}+{{\partial }^{\mu }}{{\partial }^{\nu }}\phi -{{\partial }^{\nu }}{{\partial }^{\mu }}\phi ={{F}^{\mu \nu }} \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\tilde {F}}^{\mu \nu }}={{\partial }^{\mu }}{{\tilde {\Phi }}^{\nu }}-{{\partial }^{\nu }}{{\tilde {\Phi }}^{\mu }}={{\partial }^{\mu }}\left({{\Phi }^{\nu }}+{{\partial }^{\nu }}\phi \right)-{{\partial }^{\nu }}\left({{\Phi }^{\mu }}+{{\partial }^{\mu }}\phi \right)\\&={{\partial }^{\mu }}{{\Phi }^{\nu }}-{{\partial }^{\nu }}{{\Phi }^{\mu }}+{{\partial }^{\mu }}{{\partial }^{\nu }}\phi -{{\partial }^{\nu }}{{\partial }^{\mu }}\phi ={{F}^{\mu \nu }}\\\end{aligned}}
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MathML (3.04 KB / 444 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>F</mi><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>μ</mi><mi>ν</mi></mrow></mrow></msup><mo>=</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi mathvariant="normal">Φ</mi><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mo>−</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi mathvariant="normal">Φ</mi><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mo>=</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi mathvariant="normal">Φ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mo>+</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mi>ϕ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>−</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi mathvariant="normal">Φ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mo>+</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mi>ϕ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><msup><mi mathvariant="normal">Φ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mo>−</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><msup><mi mathvariant="normal">Φ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mo>+</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mi>ϕ</mi><mo>−</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mi>ϕ</mi><mo>=</mo><msup><mi>F</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>μ</mi><mi>ν</mi></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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