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Display information for equation id:math.2684.9 on revision:2684
* Page found: Weitere Eigenschaften der Dirac-Gleichung (eq math.2684.9)
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TeX (original user input):
\begin{align}
& {{\left( {{\gamma }^{0}} \right)}^{+}}={{\gamma }^{0}},{{\left( {{\gamma }^{0}} \right)}^{2}}=1 \\
& {{\left( {{\gamma }^{k}} \right)}^{+}}=-{{\gamma }^{k}},{{\left( {{\gamma }^{k}} \right)}^{2}}=-1\quad k\in \left\{ 1,2,3 \right\} \\
& {{\gamma }^{\mu }}{{\gamma }^{\nu }}+{{\gamma }^{\nu }}{{\gamma }^{\mu }}=2{{g}^{\mu }}^{\nu },\quad {{g}^{\mu }}^{\nu }=diag\left( 1,-1,-1,-1 \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\left({{\gamma }^{0}}\right)}^{+}}={{\gamma }^{0}},{{\left({{\gamma }^{0}}\right)}^{2}}=1\\&{{\left({{\gamma }^{k}}\right)}^{+}}=-{{\gamma }^{k}},{{\left({{\gamma }^{k}}\right)}^{2}}=-1\quad k\in \left\{1,2,3\right\}\\&{{\gamma }^{\mu }}{{\gamma }^{\nu }}+{{\gamma }^{\nu }}{{\gamma }^{\mu }}=2{{g}^{\mu }}^{\nu },\quad {{g}^{\mu }}^{\nu }=diag\left(1,-1,-1,-1\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"><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">+</mo></mrow></msup><mo stretchy="false">=</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo>,</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">=</mo><mn>1</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">+</mo></mrow></msup><mo stretchy="false">=</mo><mo stretchy="false">−</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msup><mo>,</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mn>1</mn><mspace width="1em"></mspace><mi>k</mi><mo stretchy="false">∈</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo data-mjx-texclass="CLOSE">}</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mo stretchy="false">+</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mo stretchy="false">=</mo><mn>2</mn><msup><msup><mi>g</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mo>,</mo><mspace width="1em"></mspace><msup><msup><mi>g</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mo stretchy="false">=</mo><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo>,</mo><mo stretchy="false">−</mo><mn>1</mn><mo>,</mo><mo stretchy="false">−</mo><mn>1</mn><mo>,</mo><mo stretchy="false">−</mo><mn>1</mn><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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