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Display information for equation id:math.1199.1275 on revision:1199

* Page found: Elektrodynamik Schöll (eq math.1199.1275)

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Relativistisches Hamiltonprinzip Eq: math.2176.17

Hash: bf760ff9bffd112f1007cf5feb74dc44

TeX (original user input):

\begin{align}
& {{p}^{\mu }}={{m}_{0}}c{{u}^{\mu }} \\
& {{f}^{\mu \nu }}=\frac{q}{c}{{F}^{\mu \nu }}=\left( {{\partial }^{\mu }}{{\phi }^{\nu }}-{{\partial }^{\nu }}{{\phi }^{\mu }} \right) \\
& {{\phi }^{\mu }}=\frac{q}{c}{{\Phi }^{\mu }} \\
& \frac{d}{ds}{{p}^{\mu }}=\frac{q}{c}{{F}^{\mu \nu }}{{u}_{\nu }}\Leftrightarrow \delta W=\delta \int_{1}^{2}{{}}\left\{ -{{m}_{0}}cds-\frac{q}{c}{{\Phi }^{\mu }}d{{x}_{\mu }} \right\}=0 \\
\end{align}

TeX (checked):

{\begin{aligned}&{{p}^{\mu }}={{m}_{0}}c{{u}^{\mu }}\\&{{f}^{\mu \nu }}={\frac {q}{c}}{{F}^{\mu \nu }}=\left({{\partial }^{\mu }}{{\phi }^{\nu }}-{{\partial }^{\nu }}{{\phi }^{\mu }}\right)\\&{{\phi }^{\mu }}={\frac {q}{c}}{{\Phi }^{\mu }}\\&{\frac {d}{ds}}{{p}^{\mu }}={\frac {q}{c}}{{F}^{\mu \nu }}{{u}_{\nu }}\Leftrightarrow \delta W=\delta \int _{1}^{2}{}\left\{-{{m}_{0}}cds-{\frac {q}{c}}{{\Phi }^{\mu }}d{{x}_{\mu }}\right\}=0\\\end{aligned}}

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\begin{aligned} p^{μ} = m_{0} c u^{μ} \\ f^{μ ν} = \frac{q}{c} F^{μ ν} = (\partial^{μ} ϕ^{ν} - \partial^{ν} ϕ^{μ}) \\ ϕ^{μ} = \frac{q}{c} Φ^{μ} \\ \frac{d}{d s} p^{μ} = \frac{q}{c} F^{μ ν} u_{ν} \Leftrightarrow δ W = δ \int_{1}^{2} {- m_{0} c d s - \frac{q}{c} Φ^{μ} d x_{μ}} = 0 \end{aligned}

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Identifiers

$p$

$μ$

$m_{0}$

$c$

$u$

$μ$

$f$

$μ$

$ν$

$q$

$c$

$F$

$μ$

$ν$

$μ$

$ϕ$

$ν$

$ν$

$ϕ$

$μ$

$ϕ$

$μ$

$q$

$c$

$Φ$

$μ$

$d$

$d$

$s$

$p$

$μ$

$q$

$c$

$F$

$μ$

$ν$

$u_{ν}$

$δ$

$W$

$δ$

$m_{0}$

$c$

$s$

$q$

$c$

$Φ$

$μ$

$d$

$x_{μ}$

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