Summary of 4-momentum components

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[math]\textbf{\underline{Navigation}}[/math]

[math]\vartriangleleft [/math] [math]\triangle [/math] [math]\vartriangleright [/math]


Summary of 4-momentum components

[math]For\ 0 \ge \phi \ge \frac{-\pi}{2}\ Radians[/math]
x=POSITIVE
y=NEGATIVE
[math]For\ 0 \le \phi \le \frac{\pi}{2}\ Radians[/math]
x=POSITIVE
y=POSITIVE
[math]For\ \frac{-\pi}{2} \ge \phi \ge -\pi\ Radians[/math]
x=NEGATIVE
y=NEGATIVE
[math]For\ \frac{\pi}{2} \le \phi \le \pi\ Radians[/math]
x=NEGATIVE
y=POSITIVE


4 momentum calculations for different frames of reference
Electron Initial Lab Frame Moller electron Initial Lab Frame Moller electron Final Lab Frame Moller electron Center of Mass Frame Electron Center of Mass Frame Electron Final Lab Frame
[math]p_{1}\equiv 11000 MeV[/math] [math]p_{2}\equiv 0[/math] [math]p_{2}'\equiv INPUT[/math] [math]p_{2}^*=\sqrt{E_{2}^{*2}-m^2}[/math] [math]p_{1}^*=\sqrt{E_{2}^{*2}-m^2}[/math] [math]p_{1}'=\sqrt{E_{1}^{'\ 2}-m^2}[/math]
[math]\theta_{1}\equiv 0[/math] [math]\theta_{2}\equiv 0[/math] [math]\theta_{2}'\equiv INPUT[/math] [math]\theta_{2}^*=\arccos \left(\frac{p_{2(z)}^*}{p_2^*} \right)[/math] [math]\theta_{1}^*=\pi-\theta_{2}^*[/math] [math]\theta_{1}'= \arccos \left(\frac{p_{1(z)}'}{p_{1}'} \right)[/math]
[math]E_{1}=\sqrt{p_1^2+m^2}[/math] [math]E_{2}\equiv m[/math] [math]E_{2}'=\sqrt{p_{2}^{'\ 2}+m^2}[/math] [math]E_{2}^*=\sqrt{\frac{m(m+E_1)}{2}}[/math] [math]E_{1}^*=\sqrt{\frac{m(m+E_1)}{2}}[/math] [math]E_{1}'\equiv E'-E_{2}'[/math]
[math]p_{1(x)}\equiv 0[/math] [math]p_{2(x)}\equiv 0[/math] [math]p_{2(x)}'=\sqrt{p_{2}^{'\ 2}-p_{2(z)}^{'\ 2}} cos(\phi '_2)[/math] [math]p_{2(x)}^*\equiv p_{2(x)}'[/math] [math]p_{1(x)}^*\equiv-p_{2(x)}^*[/math] [math]p_{1(x)}'\equiv p_{1(x)}^*[/math]
[math]p_{1(y)}\equiv 0[/math] [math]p_{2(y)}\equiv 0[/math] [math]p_{2(y)}'=\sqrt{p_{2}^{'\ 2}-p_{2(x)}^{'\ 2}-p_{2(z)}^{'\ 2}}[/math] [math]p_{2(y)}^*\equiv p_{2(y)}'[/math] [math]p_{1(y)}^*\equiv -p_{2(y)}^*[/math] [math]p_{1(y)}'\equiv p_{2(y)}^*[/math]
[math]p_{1(z)}\equiv p_1[/math] [math]p_{2(z)}\equiv 0[/math] [math]p_{2(z)}'\equiv p_{2}'\ cos(\theta'_2)[/math] [math]p_{2(z)}^*=-\sqrt{p_{2}^{*\ 2}-p_{2(x)}^{*\ 2}-p_{2(y)}^{*\ 2}}[/math] [math]p_{1(z)}^*\equiv -p_{2(z)}^*[/math] [math]p_{1(z)}'=\sqrt{p_{1}^{'\ 2}-p_{(1(x)}^{'\ 2}-p_{1(y)}^{'\ 2}}[/math]




[math]\textbf{\underline{Navigation}}[/math]

[math]\vartriangleleft [/math] [math]\triangle [/math] [math]\vartriangleright [/math]