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Display information for equation id:math.2679.10 on revision:2679

* Page found: Dirac-Gleichung und Spin: nichtrelativistischer Grenzfall (eq math.2679.10)

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\begin{align}

& \left\{ {{{\underline{\underline{\sigma }}}}_{i}},{{{\underline{\underline{\sigma }}}}_{j}} \right\}:={{{\underline{\underline{\sigma }}}}_{i}}{{{\underline{\underline{\sigma }}}}_{j}}+{{{\underline{\underline{\sigma }}}}_{j}}{{{\underline{\underline{\sigma }}}}_{i}}=2{{\delta }_{ij}}\underline{\underline{1}} \\

& \left[ {{{\underline{\underline{\sigma }}}}_{i}},{{{\underline{\underline{\sigma }}}}_{j}} \right]:={{{\underline{\underline{\sigma }}}}_{i}}{{{\underline{\underline{\sigma }}}}_{j}}-{{{\underline{\underline{\sigma }}}}_{j}}{{{\underline{\underline{\sigma }}}}_{i}}=2\mathfrak{i} {{\varepsilon }_{ijk}}{{{\underline{\underline{\sigma }}}}_{k}} \\

\end{align}

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MathML (34.532 KB / 3.493 KB) :

{ σ ¯ ¯ i , σ ¯ ¯ j } := σ ¯ ¯ i σ ¯ ¯ j + σ ¯ ¯ j σ ¯ ¯ i = 2 δ i j 1 ¯ ¯ [ σ ¯ ¯ i , σ ¯ ¯ j ] := σ ¯ ¯ i σ ¯ ¯ j - σ ¯ ¯ j σ ¯ ¯ i = 2 𝔦 ε i j k σ ¯ ¯ k absent assign subscript ¯ ¯ 𝜎 𝑖 subscript ¯ ¯ 𝜎 𝑗 subscript ¯ ¯ 𝜎 𝑖 subscript ¯ ¯ 𝜎 𝑗 subscript ¯ ¯ 𝜎 𝑗 subscript ¯ ¯ 𝜎 𝑖 2 subscript 𝛿 𝑖 𝑗 ¯ ¯ 1 absent assign subscript ¯ ¯ 𝜎 𝑖 subscript ¯ ¯ 𝜎 𝑗 subscript ¯ ¯ 𝜎 𝑖 subscript ¯ ¯ 𝜎 𝑗 subscript ¯ ¯ 𝜎 𝑗 subscript ¯ ¯ 𝜎 𝑖 2 𝔦 subscript 𝜀 𝑖 𝑗 𝑘 subscript ¯ ¯ 𝜎 𝑘 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle\left\{{{{% \underline{\underline{\sigma}}}}_{i}},{{{\underline{\underline{\sigma}}}}_{j}}% \right\}:={{{\underline{\underline{\sigma}}}}_{i}}{{{\underline{\underline{% \sigma}}}}_{j}}+{{{\underline{\underline{\sigma}}}}_{j}}{{{\underline{% \underline{\sigma}}}}_{i}}=2{{\delta}_{ij}}\underline{\underline{1}}\\ \par&\displaystyle\left[{{{\underline{\underline{\sigma}}}}_{i}},{{{\underline% {\underline{\sigma}}}}_{j}}\right]:={{{\underline{\underline{\sigma}}}}_{i}}{{% {\underline{\underline{\sigma}}}}_{j}}-{{{\underline{\underline{\sigma}}}}_{j}% }{{{\underline{\underline{\sigma}}}}_{i}}=2\mathfrak{i}{{\varepsilon}_{ijk}}{{% {\underline{\underline{\sigma}}}}_{k}}\\ \par\end{aligned}}}

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{σ__i,σ__j}:=σ__iσ__j+σ__jσ__i=2δij1__[σ__i,σ__j]:=σ__iσ__jσ__jσ__i=2iεijkσ__k

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