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* Page found: Dirac- Gleichung für Elektronen (eq math.1807.62)

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Dirac- Gleichung für Elektronen Eq: math.1807.62

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TeX (original user input):

\begin{align}

& {{j}^{0}}=c{{\Psi }^{+}}\Psi =c\sum\limits_{s=1}^{4}{{{\Psi }_{S}}^{*}{{\Psi }_{S}}=c\rho } \\

& {{j}^{\mu }}=c\left( {{\Psi }^{+}}{{\alpha }^{\mu }}\Psi  \right)=c\sum\limits_{s,s\acute{\ }}^{{}}{{}}{{\Psi }_{S}}*{{\alpha }_{SS\acute{\ }}}^{\mu }{{\Psi }_{S\acute{\ }}}\quad \mu =1,2,3 \\

\end{align}

TeX (checked):

{\begin{aligned}&{{j}^{0}}=c{{\Psi }^{+}}\Psi =c\sum \limits _{s=1}^{4}{{{\Psi }_{S}}^{*}{{\Psi }_{S}}=c\rho }\\&{{j}^{\mu }}=c\left({{\Psi }^{+}}{{\alpha }^{\mu }}\Psi \right)=c\sum \limits _{s,s{\acute {\ }}}^{}{}{{\Psi }_{S}}*{{\alpha }_{SS{\acute {\ }}}}^{\mu }{{\Psi }_{S{\acute {\ }}}}\quad \mu =1,2,3\\\end{aligned}}

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\begin{aligned} j^{0} = c Ψ^{+} Ψ = c \sum_{s = 1}^{4} {Ψ_{S}}^{*} Ψ_{S} = c ρ \\ j^{μ} = c (Ψ^{+} α^{μ} Ψ) = c \sum_{s, s \overset{´}{}}^{} Ψ_{S} * {α_{S S \overset{´}{}}}^{μ} Ψ_{S \overset{´}{}} μ = 1, 2, 3 \end{aligned}

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Identifiers

$j$

$c$

$Ψ$

$Ψ$

$c$

$s$

$Ψ_{S}$

$Ψ_{S}$

$c$

$ρ$

$j$

$μ$

$c$

$Ψ$

$α$

$μ$

$Ψ$

$c$

$s$

$s$

$\overset{´}{}$

$Ψ_{S}$

$α$

$S$

$S$

$\overset{´}{}$

$μ$

$Ψ$

$S$

$\overset{´}{}$

$μ$

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