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Display information for equation id:math.1109.221 on revision:1109
* Page found: ART-Skript (eq math.1109.221)
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Hash: bc2d9f34f37c157f7b5a4e7994edf968
TeX (original user input):
\begin{align}
& d{{\xi }^{\alpha }}\to d{{x}^{\alpha }}=\frac{\partial {{x}^{\alpha }}}{d{{\xi }^{\mu }}}d{{\xi }^{\mu }} \\
& {{\eta }_{\mu \nu }}\to {{g}_{\mu \nu }}={{\eta }_{\alpha \beta }}\frac{\partial {{\xi }^{\alpha }}}{\partial {{x}^{\mu }}}\frac{\partial {{\xi }^{\beta }}}{\partial {{x}^{\nu }}} \\
& A_{{{M}_{4}}}^{\alpha }\to A_{{{V}_{4}}}^{\alpha }=\frac{\partial {{x}^{\alpha }}}{\partial {{\xi }^{\mu }}}A_{{{M}_{4}}}^{\mu } \\
\end{align}
TeX (checked):
{\begin{aligned}&d{{\xi }^{\alpha }}\to d{{x}^{\alpha }}={\frac {\partial {{x}^{\alpha }}}{d{{\xi }^{\mu }}}}d{{\xi }^{\mu }}\\&{{\eta }_{\mu \nu }}\to {{g}_{\mu \nu }}={{\eta }_{\alpha \beta }}{\frac {\partial {{\xi }^{\alpha }}}{\partial {{x}^{\mu }}}}{\frac {\partial {{\xi }^{\beta }}}{\partial {{x}^{\nu }}}}\\&A_{{M}_{4}}^{\alpha }\to A_{{V}_{4}}^{\alpha }={\frac {\partial {{x}^{\alpha }}}{\partial {{\xi }^{\mu }}}}A_{{M}_{4}}^{\mu }\\\end{aligned}}
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<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><mi>d</mi><msup><mi>ξ</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup><mo accent="false">→</mo><mi>d</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><msup><mi>ξ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup></mrow></mrow></mfrac></mrow><mi>d</mi><msup><mi>ξ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><msub><mi>η</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>μ</mi><mi>ν</mi></mrow></mrow></msub><mo accent="false">→</mo><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>μ</mi><mi>ν</mi></mrow></mrow></msub><mo>=</mo><msub><mi>η</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>α</mi><mi>β</mi></mrow></mrow></msub><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>ξ</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>ξ</mi><mrow data-mjx-texclass="ORD"><mi>β</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd><mtd><msubsup><mi>A</mi><mrow data-mjx-texclass="ORD"><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msubsup><mo accent="false">→</mo><msubsup><mi>A</mi><mrow data-mjx-texclass="ORD"><msub><mi>V</mi><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msubsup><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>ξ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup></mrow></mrow></mfrac></mrow><msubsup><mi>A</mi><mrow data-mjx-texclass="ORD"><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msubsup></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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