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Display information for equation id:math.1446.113 on revision:1446
* Page found: Relativistische Formulierung der Elektrodynamik (eq math.1446.113)
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TeX (original user input):
\begin{align}
& \delta W=\int_{1}^{2}{{}}\left\{ {{m}_{0}}c\frac{d{{u}^{\mu }}}{ds}-\left( {{\partial }^{\mu }}{{\phi }^{\nu }}-{{\partial }^{\nu }}{{\phi }^{\mu }} \right){{u}_{\nu }} \right\}\delta {{x}_{\mu }}=0 \\
& {{m}_{0}}c\frac{d{{u}^{\mu }}}{ds}=\left( {{\partial }^{\mu }}{{\phi }^{\nu }}-{{\partial }^{\nu }}{{\phi }^{\mu }} \right){{u}_{\nu }}:={{f}^{\mu \nu }}{{u}_{\nu }} \\
& {{f}^{\mu \nu }}=\left( {{\partial }^{\mu }}{{\phi }^{\nu }}-{{\partial }^{\nu }}{{\phi }^{\mu }} \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&\delta W=\int _{1}^{2}{}\left\{{{m}_{0}}c{\frac {d{{u}^{\mu }}}{ds}}-\left({{\partial }^{\mu }}{{\phi }^{\nu }}-{{\partial }^{\nu }}{{\phi }^{\mu }}\right){{u}_{\nu }}\right\}\delta {{x}_{\mu }}=0\\&{{m}_{0}}c{\frac {d{{u}^{\mu }}}{ds}}=\left({{\partial }^{\mu }}{{\phi }^{\nu }}-{{\partial }^{\nu }}{{\phi }^{\mu }}\right){{u}_{\nu }}:={{f}^{\mu \nu }}{{u}_{\nu }}\\&{{f}^{\mu \nu }}=\left({{\partial }^{\mu }}{{\phi }^{\nu }}-{{\partial }^{\nu }}{{\phi }^{\mu }}\right)\\\end{aligned}}
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<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>δ</mi><mi>W</mi><mo stretchy="false">=</mo><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msubsup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><msup><mi>u</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>s</mi></mrow></mrow></mfrac></mrow><mo stretchy="false">−</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><msup><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mo stretchy="false">−</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><msup><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><msub><mi>u</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mo data-mjx-texclass="CLOSE">}</mo></mrow><mi>δ</mi><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msub><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><msup><mi>u</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>s</mi></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><msup><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mo stretchy="false">−</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><msup><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><msub><mi>u</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mo stretchy="false">:=</mo><msup><mi>f</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>μ</mi><mi>ν</mi></mrow></mrow></msup><msub><mi>u</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msup><mi>f</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>μ</mi><mi>ν</mi></mrow></mrow></msup><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><msup><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mo stretchy="false">−</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><msup><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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