Summary of 4-momentum components

Summary of 4-momentum components

[math]\displaystyle{ For\ 0 \ge \phi \ge \frac{-\pi}{2}\ Radians }[/math]

x=POSITIVE

y=NEGATIVE

[math]\displaystyle{ For\ 0 \le \phi \le \frac{\pi}{2}\ Radians }[/math]

x=POSITIVE

y=POSITIVE

[math]\displaystyle{ For\ \frac{-\pi}{2} \ge \phi \ge -\pi\ Radians }[/math]

x=NEGATIVE

y=NEGATIVE

[math]\displaystyle{ 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]\displaystyle{ p_{1}\equiv 11000 MeV }[/math]	[math]\displaystyle{ p_{2}\equiv 0 }[/math]	[math]\displaystyle{ p_{2}'\equiv INPUT }[/math]	[math]\displaystyle{ p_{2}^*=\sqrt{E_{2}^{*2}-m^2} }[/math]	[math]\displaystyle{ p_{1}^*=\sqrt{E_{2}^{*2}-m^2} }[/math]	[math]\displaystyle{ p_{1}'=\sqrt{E_{1}^{'\ 2}-m^2} }[/math]
[math]\displaystyle{ \theta_{1}\equiv 0 }[/math]	[math]\displaystyle{ \theta_{2}\equiv 0 }[/math]	[math]\displaystyle{ \theta_{2}'\equiv INPUT }[/math]	[math]\displaystyle{ \theta_{2}^*=\arccos \left(\frac{p_{2(z)}^*}{p_2^*} \right) }[/math]	[math]\displaystyle{ \theta_{1}^*=\pi-\theta_{2}^* }[/math]	[math]\displaystyle{ \theta_{1}'= \arccos \left(\frac{p_{1(z)}'}{p_{1}'} \right) }[/math]
[math]\displaystyle{ E_{1}=\sqrt{p_1^2+m^2} }[/math]	[math]\displaystyle{ E_{2}\equiv m }[/math]	[math]\displaystyle{ E_{2}'=\sqrt{p_{2}^{'\ 2}+m^2} }[/math]	[math]\displaystyle{ E_{2}^*=\sqrt{\frac{m(m+E_1)}{2}} }[/math]	[math]\displaystyle{ E_{1}^*=\sqrt{\frac{m(m+E_1)}{2}} }[/math]	[math]\displaystyle{ E_{1}'\equiv E'-E_{2}' }[/math]
[math]\displaystyle{ p_{1(x)}\equiv 0 }[/math]	[math]\displaystyle{ p_{2(x)}\equiv 0 }[/math]	[math]\displaystyle{ p_{2(x)}'=\sqrt{p_{2}^{'\ 2}-p_{2(z)}^{'\ 2}} cos(\phi '_2) }[/math]	[math]\displaystyle{ p_{2(x)}^*\equiv p_{2(x)}' }[/math]	[math]\displaystyle{ p_{1(x)}^*\equiv-p_{2(x)}^* }[/math]	[math]\displaystyle{ p_{1(x)}'\equiv p_{1(x)}^* }[/math]
[math]\displaystyle{ p_{1(y)}\equiv 0 }[/math]	[math]\displaystyle{ p_{2(y)}\equiv 0 }[/math]	[math]\displaystyle{ p_{2(y)}'=\sqrt{p_{2}^{'\ 2}-p_{2(x)}^{'\ 2}-p_{2(z)}^{'\ 2}} }[/math]	[math]\displaystyle{ p_{2(y)}^*\equiv p_{2(y)}' }[/math]	[math]\displaystyle{ p_{1(y)}^*\equiv -p_{2(y)}^* }[/math]	[math]\displaystyle{ p_{1(y)}'\equiv p_{2(y)}^* }[/math]
[math]\displaystyle{ p_{1(z)}\equiv p_1 }[/math]	[math]\displaystyle{ p_{2(z)}\equiv 0 }[/math]	[math]\displaystyle{ p_{2(z)}'\equiv p_{2}'\ cos(\theta'_2) }[/math]	[math]\displaystyle{ p_{2(z)}^*=-\sqrt{p_{2}^{*\ 2}-p_{2(x)}^{*\ 2}-p_{2(y)}^{*\ 2}} }[/math]	[math]\displaystyle{ p_{1(z)}^*\equiv -p_{2(z)}^* }[/math]	[math]\displaystyle{ p_{1(z)}'=\sqrt{p_{1}^{'\ 2}-p_{(1(x)}^{'\ 2}-p_{1(y)}^{'\ 2}} }[/math]