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* Page found: Weitere Eigenschaften der Dirac-Gleichung (eq math.2685.37)
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S\left ( \beta \right )=\underline { \underline { 1}} +\frac { \beta }{ 2}{{ \gamma }^{ 1}}{{ \gamma }^{ 0}} +O\left ( {{ \beta }^{ 2}} \right )=\left ( \begin { matrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end { matrix} \right )+\frac { \beta }{ 2} \left ( \begin { matrix}
0 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 \\
0 & 1 & 0 & 0 \\
1 & 0 & 0 & 0 \\
\end { matrix} \right )+O\left ( {{ \beta }^{ 2}} \right )
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MathML (experimentell; keine Bilder) rendering Ausklappen MathML (2.506 KB / 400 B) :
S ( β ) = 1 _ _ + β 2 γ 1 γ 0 + O ( β 2 ) = ( 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ) + β 2 ( 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 ) + O ( β 2 ) <math class= "mwe-math-element" xmlns= "http://www.w3.org/1998/Math/MathML" ><mrow data-mjx-texclass= "ORD" ><mstyle displaystyle= "true" scriptlevel= "0" ><mi> S</mi><mrow data-mjx-texclass= "INNER" ><mo data-mjx-texclass= "OPEN" > (</mo><mi> β </mi><mo data-mjx-texclass= "CLOSE" > )</mo></mrow><mo> =</mo><mrow data-mjx-texclass= "ORD" ><munder><mrow data-mjx-texclass= "ORD" ><munder><mn> 1</mn><mo> _</mo></munder></mrow><mo> _</mo></munder></mrow><mo> +</mo><mrow data-mjx-texclass= "ORD" ><mfrac><mrow data-mjx-texclass= "ORD" ><mi> β </mi></mrow><mrow data-mjx-texclass= "ORD" ><mn> 2</mn></mrow></mfrac></mrow><msup><mi> γ </mi><mrow data-mjx-texclass= "ORD" ><mn> 1</mn></mrow></msup><msup><mi> γ </mi><mrow data-mjx-texclass= "ORD" ><mn> 0</mn></mrow></msup><mo> +</mo><mi> O</mi><mrow data-mjx-texclass= "INNER" ><mo data-mjx-texclass= "OPEN" > (</mo><msup><mi> β </mi><mrow data-mjx-texclass= "ORD" ><mn> 2</mn></mrow></msup><mo data-mjx-texclass= "CLOSE" > )</mo></mrow><mo> =</mo><mrow data-mjx-texclass= "INNER" ><mo data-mjx-texclass= "OPEN" > (</mo><mrow data-mjx-texclass= "ORD" ><mtable columnspacing= "1em" rowspacing= "4pt" ><mtr><mtd><mn> 1</mn></mtd><mtd><mn> 0</mn></mtd><mtd><mn> 0</mn></mtd><mtd><mn> 0</mn></mtd></mtr><mtr><mtd><mn> 0</mn></mtd><mtd><mn> 1</mn></mtd><mtd><mn> 0</mn></mtd><mtd><mn> 0</mn></mtd></mtr><mtr><mtd><mn> 0</mn></mtd><mtd><mn> 0</mn></mtd><mtd><mn> 1</mn></mtd><mtd><mn> 0</mn></mtd></mtr><mtr><mtd><mn> 0</mn></mtd><mtd><mn> 0</mn></mtd><mtd><mn> 0</mn></mtd><mtd><mn> 1</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass= "CLOSE" > )</mo></mrow><mo> +</mo><mrow data-mjx-texclass= "ORD" ><mfrac><mrow data-mjx-texclass= "ORD" ><mi> β </mi></mrow><mrow data-mjx-texclass= "ORD" ><mn> 2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass= "INNER" ><mo data-mjx-texclass= "OPEN" > (</mo><mrow data-mjx-texclass= "ORD" ><mtable columnspacing= "1em" rowspacing= "4pt" ><mtr><mtd><mn> 0</mn></mtd><mtd><mn> 0</mn></mtd><mtd><mn> 0</mn></mtd><mtd><mn> 1</mn></mtd></mtr><mtr><mtd><mn> 0</mn></mtd><mtd><mn> 0</mn></mtd><mtd><mn> 1</mn></mtd><mtd><mn> 0</mn></mtd></mtr><mtr><mtd><mn> 0</mn></mtd><mtd><mn> 1</mn></mtd><mtd><mn> 0</mn></mtd><mtd><mn> 0</mn></mtd></mtr><mtr><mtd><mn> 1</mn></mtd><mtd><mn> 0</mn></mtd><mtd><mn> 0</mn></mtd><mtd><mn> 0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass= "CLOSE" > )</mo></mrow><mo> +</mo><mi> O</mi><mrow data-mjx-texclass= "INNER" ><mo data-mjx-texclass= "OPEN" > (</mo><msup><mi> β </mi><mrow data-mjx-texclass= "ORD" ><mn> 2</mn></mrow></msup><mo data-mjx-texclass= "CLOSE" > )</mo></mrow></mstyle></mrow></math>
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