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* Page found: Weitere Eigenschaften der Dirac-Gleichung (eq math.2682.9)

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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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MathML (28.459 KB / 3.067 KB) :

( γ 0 ) + = γ 0 , ( γ 0 ) 2 = 1 ( γ k ) + = - γ k , ( γ k ) 2 = - 1   k ∈ { 1 , 2 , 3 } γ μ ⁢ γ ν + γ ν ⁢ γ μ = 2 ⁢ g μ ν , g μ ν = d ⁢ i ⁢ a ⁢ g ⁢ ( 1 , - 1 , - 1 , - 1 ) absent formulae-sequence superscript superscript 𝛾 0 superscript 𝛾 0 superscript superscript 𝛾 0 2 1 absent formulae-sequence superscript superscript 𝛾 𝑘 superscript 𝛾 𝑘 formulae-sequence superscript superscript 𝛾 𝑘 2 1 𝑘 1 2 3 absent formulae-sequence superscript 𝛾 𝜇 superscript 𝛾 𝜈 superscript 𝛾 𝜈 superscript 𝛾 𝜇 2 superscript superscript 𝑔 𝜇 𝜈 superscript superscript 𝑔 𝜇 𝜈 𝑑 𝑖 𝑎 𝑔 1 1 1 1 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle{{\left({{\gamma% }^{0}}\right)}^{+}}={{\gamma}^{0}},{{\left({{\gamma}^{0}}\right)}^{2}}=1\\ \par&\displaystyle{{\left({{\gamma}^{k}}\right)}^{+}}=-{{\gamma}^{k}},{{\left(% {{\gamma}^{k}}\right)}^{2}}=-1\quad k\in\left\{1,2,3\right\}\\ \par&\displaystyle{{\gamma}^{\mu}}{{\gamma}^{\nu}}+{{\gamma}^{\nu}}{{\gamma}^{% \mu}}=2{{g}^{\mu}}^{\nu},\quad{{g}^{\mu}}^{\nu}=diag\left(1,-1,-1,-1\right)\\ \par\end{aligned}}}

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MathML (2.899 KB / 474 B) :

(γ0)+=γ0,(γ0)2=1(γk)+=−γk,(γk)2=−1k∈{1,2,3}γμγν+γνγμ=2gμν,gμν=diag(1,−1,−1,−1)

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