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Display information for equation id:math.2659.31 on revision:2659

* Page found: Klein Gordon im (Vektor)Potential, Eichinvarianz (eq math.2659.31)

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Klein Gordon im (Vektor)Potential, Eichinvarianz Eq: math.2665.31

Hash: 3697350916e03c9fd438ca58c8a7a958

TeX (original user input):

\begin{align}

& {{{\underline{D}}}_{\varphi }}=\underline{\nabla }+{{{\underline{f}}}_{\varphi }}\left( \underline{x},t \right)\quad \leftrightarrow \quad \underline{D}=\underline{\nabla }+{{{\underline{f}}}_{\varphi }}\left( \underline{x},t \right)+\mathfrak{i} \nabla \varphi \left( \underline{x},t \right) \\

& {{D}_{0}}={{\partial }_{t}}+{{g}_{\varphi }}\left( \underline{x},t \right)\quad \leftrightarrow \quad {{D}^{0}}={{\partial }_{t}}+{{g}_{\varphi }}\left( \underline{x},t \right)+\mathfrak{i} {{\partial }_{t}}\varphi \left( \underline{x},t \right) \\

\end{align}

TeX (checked):

{\begin{aligned}&{{\underline {D}}_{\varphi }}={\underline {\nabla }}+{{\underline {f}}_{\varphi }}\left({\underline {x}},t\right)\quad \leftrightarrow \quad {\underline {D}}={\underline {\nabla }}+{{\underline {f}}_{\varphi }}\left({\underline {x}},t\right)+{\mathfrak {i}}\nabla \varphi \left({\underline {x}},t\right)\\&{{D}_{0}}={{\partial }_{t}}+{{g}_{\varphi }}\left({\underline {x}},t\right)\quad \leftrightarrow \quad {{D}^{0}}={{\partial }_{t}}+{{g}_{\varphi }}\left({\underline {x}},t\right)+{\mathfrak {i}}{{\partial }_{t}}\varphi \left({\underline {x}},t\right)\\\end{aligned}}

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MathML (3.388 KB / 465 B) :

\begin{matrix} {\underline{D}}_{φ} = \underline{\nabla} + {\underline{f}}_{φ} (\underline{x}, t) \leftrightarrow \underline{D} = \underline{\nabla} + {\underline{f}}_{φ} (\underline{x}, t) + 𝔦 \nabla φ (\underline{x}, t) \\ D_{0} = \partial_{t} + g_{φ} (\underline{x}, t) \leftrightarrow D^{0} = \partial_{t} + g_{φ} (\underline{x}, t) + 𝔦 \partial_{t} φ (\underline{x}, t) \end{matrix}

<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"><msub><mrow data-mjx-texclass="ORD"><munder><mi>D</mi><mo>_</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mi>φ</mi></mrow></msub><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><munder><mi mathvariant="normal">∇</mi><mo>_</mo></munder></mrow><mo stretchy="false">+</mo><msub><mrow data-mjx-texclass="ORD"><munder><mi>f</mi><mo>_</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mi>φ</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><munder><mi>x</mi><mo>_</mo></munder></mrow><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mspace width="1em"></mspace><mo stretchy="false">↔</mo><mspace width="1em"></mspace><mrow data-mjx-texclass="ORD"><munder><mi>D</mi><mo>_</mo></munder></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><munder><mi mathvariant="normal">∇</mi><mo>_</mo></munder></mrow><mo stretchy="false">+</mo><msub><mrow data-mjx-texclass="ORD"><munder><mi>f</mi><mo>_</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mi>φ</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><munder><mi>x</mi><mo>_</mo></munder></mrow><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mi>𝔦</mi></mrow><mi mathvariant="normal">∇</mi><mi>φ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><munder><mi>x</mi><mo>_</mo></munder></mrow><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mi>D</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">=</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mo stretchy="false">+</mo><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mi>φ</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><munder><mi>x</mi><mo>_</mo></munder></mrow><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mspace width="1em"></mspace><mo stretchy="false">↔</mo><mspace width="1em"></mspace><msup><mi>D</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo stretchy="false">=</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mo stretchy="false">+</mo><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mi>φ</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><munder><mi>x</mi><mo>_</mo></munder></mrow><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mi>𝔦</mi></mrow><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mi>φ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><munder><mi>x</mi><mo>_</mo></munder></mrow><mo>,</mo><mi>t</mi><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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Identifiers

${\underline{D}}_{φ}$

${\underline{f}}_{φ}$

$\underline{x}$

$t$

$\underline{D}$

${\underline{f}}_{φ}$

$\underline{x}$

$t$

$𝔦$

$φ$

$\underline{x}$

$t$

$D_{0}$

$t$

$g_{φ}$

$\underline{x}$

$t$

$D$

$t$

$g_{φ}$

$\underline{x}$

$t$

$𝔦$

$t$

$φ$

$\underline{x}$

$t$

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