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Display information for equation id:math.2165.16 on revision:2165

* Page found: Ko- und Kontravariante Schreibweise der Relativitätstheorie (eq math.2165.16)

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Ko- und Kontravariante Schreibweise der Relativitätstheorie Eq: math.2169.16

Hash: e8c80c951e248c453ebb73d9c6f9d7aa

TeX (original user input):

\begin{align}
& {{p}^{i}}{{p}_{i}}={{m}_{0}}^{2}{{c}^{2}}{{u}^{i}}{{u}_{i}} \\
& {{u}^{i}}{{u}_{i}}=1 \\
& \Rightarrow {{p}^{i}}{{p}_{i}}={{m}_{0}}^{2}{{c}^{2}} \\
& {{p}^{0}}={{m}_{0}}\gamma c=m(v)c=\frac{E}{c} \\
& {{p}^{\alpha }}={{m}_{0}}\gamma {{v}^{\alpha }}=m(v){{v}^{\alpha }} \\
&  {{p}^{i}}{{p}_{i}}={{m}_{0}}^{2}{{c}^{2}}{{u}^{i}}{{u}_{i}}\Leftrightarrow {{E}^{2}}={{m}_{0}}^{2}{{c}^{4}}+{{c}^{2}}{{{\bar{p}}}^{2}} \\
\end{align}

TeX (checked):

{\begin{aligned}&{{p}^{i}}{{p}_{i}}={{m}_{0}}^{2}{{c}^{2}}{{u}^{i}}{{u}_{i}}\\&{{u}^{i}}{{u}_{i}}=1\\&\Rightarrow {{p}^{i}}{{p}_{i}}={{m}_{0}}^{2}{{c}^{2}}\\&{{p}^{0}}={{m}_{0}}\gamma c=m(v)c={\frac {E}{c}}\\&{{p}^{\alpha }}={{m}_{0}}\gamma {{v}^{\alpha }}=m(v){{v}^{\alpha }}\\&{{p}^{i}}{{p}_{i}}={{m}_{0}}^{2}{{c}^{2}}{{u}^{i}}{{u}_{i}}\Leftrightarrow {{E}^{2}}={{m}_{0}}^{2}{{c}^{4}}+{{c}^{2}}{{\bar {p}}^{2}}\\\end{aligned}}

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\begin{matrix} p^{i} p_{i} = {m_{0}}^{2} c^{2} u^{i} u_{i} \\ u^{i} u_{i} = 1 \\ \Rightarrow p^{i} p_{i} = {m_{0}}^{2} c^{2} \\ p^{0} = m_{0} γ c = m (v) c = \frac{E}{c} \\ p^{α} = m_{0} γ v^{α} = m (v) v^{α} \\ p^{i} p_{i} = {m_{0}}^{2} c^{2} u^{i} u_{i} \Leftrightarrow E^{2} = {m_{0}}^{2} c^{4} + c^{2} {\bar{p}}^{2} \end{matrix}

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Identifiers

$p$

$i$

$p_{i}$

$m_{0}$

$c$

$u$

$i$

$u_{i}$

$u$

$i$

$u_{i}$

$p$

$i$

$p_{i}$

$m_{0}$

$c$

$p$

$m_{0}$

$γ$

$c$

$m$

$v$

$c$

$E$

$c$

$p$

$α$

$m_{0}$

$γ$

$v$

$α$

$m$

$v$

$v$

$α$

$p$

$i$

$p_{i}$

$m_{0}$

$c$

$u$

$i$

$u_{i}$

$E$

$m_{0}$

$c$

$c$

$\bar{p}$

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