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Display information for equation id:math.2169.16 on revision:2169

* Page found: Ko- und Kontravariante Schreibweise der Relativitätstheorie (eq math.2169.16)

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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}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (41.458 KB / 4.37 KB) :

p i ⁢ p i = m 0 2 ⁢ c 2 ⁢ u i ⁢ u i u i ⁢ u i = 1 ⇒ p i ⁢ p i = m 0 2 ⁢ c 2 p 0 = 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 2 ⁢ c 2 ⁢ u i ⁢ u i ⇔ E 2 = m 0 2 ⁢ c 4 + c 2 ⁢ p ¯ 2 missing-subexpression superscript 𝑝 𝑖 subscript 𝑝 𝑖 superscript subscript 𝑚 0 2 superscript 𝑐 2 superscript 𝑢 𝑖 subscript 𝑢 𝑖 missing-subexpression superscript 𝑢 𝑖 subscript 𝑢 𝑖 1 missing-subexpression ⇒ absent superscript 𝑝 𝑖 subscript 𝑝 𝑖 superscript subscript 𝑚 0 2 superscript 𝑐 2 missing-subexpression superscript 𝑝 0 subscript 𝑚 0 𝛾 𝑐 𝑚 𝑣 𝑐 𝐸 𝑐 missing-subexpression superscript 𝑝 𝛼 subscript 𝑚 0 𝛾 superscript 𝑣 𝛼 𝑚 𝑣 superscript 𝑣 𝛼 missing-subexpression ⇔ superscript 𝑝 𝑖 subscript 𝑝 𝑖 superscript subscript 𝑚 0 2 superscript 𝑐 2 superscript 𝑢 𝑖 subscript 𝑢 𝑖 superscript 𝐸 2 superscript subscript 𝑚 0 2 superscript 𝑐 4 superscript 𝑐 2 superscript ¯ 𝑝 2 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle{{p}^{i}}{{p}_{i}}={% {m}_{0}}^{2}{{c}^{2}}{{u}^{i}}{{u}_{i}}\\ &\displaystyle{{u}^{i}}{{u}_{i}}=1\\ &\displaystyle\Rightarrow{{p}^{i}}{{p}_{i}}={{m}_{0}}^{2}{{c}^{2}}\\ &\displaystyle{{p}^{0}}={{m}_{0}}\gamma c=m(v)c=\frac{E}{c}\\ &\displaystyle{{p}^{\alpha}}={{m}_{0}}\gamma{{v}^{\alpha}}=m(v){{v}^{\alpha}}% \\ &\displaystyle{{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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MathML (3.433 KB / 479 B) :

pipi=m02c2uiuiuiui=1⇒pipi=m02c2p0=m0γc=m(v)c=Ecpα=m0γvα=m(v)vαpipi=m02c2uiui⇔E2=m02c4+c2p¯2

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