Total 4-momentum - Revision history

Vanwdani: /* Total 4-momentum */

2017-06-08T20:06:32Z

Total 4-momentum

Vanwdani: /* Total 4-momentum */

2017-06-08T16:55:00Z

Total 4-momentum

Vanwdani: Created page with "=Total 4-momentum= As was shown earlier the scalar product of a 4-Momentum vector with itself ,
2017-05-31T20:42:15Z

Created page with "=Total 4-momentum= As was shown earlier the scalar product of a 4-Momentum vector with itself , <center><math…"

New page
=Total 4-momentum=
As was [[DV_Calculations_of_4-momentum_components#4-Momentum_Invariants | shown earlier]] the scalar product of a 4-Momentum vector with itself ,
<center><math>{\mathbf P_1}\cdot {\mathbf P^1}=E_1E_1-\vec p_1\cdot \vec p_1 =m_{1}^2=s</math></center> ,

and the length of a 4-Momentum vector composed of 4-Momentum vectors,

<center><math>{\mathbf P^2}=({\mathbf P_1}+{\mathbf P_2})^2=(E_1+E_2)^2-(\vec p_1 +\vec p_2 )^2=(m_1+m_2)^2=s</math></center>,

are invariant quantities.

It was [[DV_Calculations_of_4-momentum_components#Equal_masses | further shown ]] that

<center><math>{\mathbf P^}^2={\mathbf P}^2</math></center>

<center>''where'' <math>{\mathbf P^}=({\mathbf P_1^}+{\mathbf P_2^})^2</math> ''represents the 4-Momentum Vector in the CM frame''</center>

<center> ''and'' <math>{\mathbf P}=({\mathbf P_1}+{\mathbf P_2})^2</math> ''represents the 4-Momentum Vector in the initial Lab frame''</center>

which can be expanded to

<center><math>{\mathbf P^}^2={\mathbf P^{'}}^2={\mathbf P}^2={\mathbf P^'}^2</math></center>

<center>''where'' <math>{\mathbf P^'}=({\mathbf P_1^'}+{\mathbf P_2^'})^2</math> ''represents the 4-Momentum Vector in the final Lab frame''</center>

<center>''and'' <math>{\mathbf P^{'}}=({\mathbf P_1^{'}}+{\mathbf P_2^{'*}})^2</math> ''represents the 4-Momentum Vector in the final CM frame''</center>

← Older revision		Revision as of 20:06, 8 June 2017
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−	~~=Total 4-momentum=~~
−	~~As was [[DV_Calculations_of_4-momentum_components#4-Momentum_Invariants \| shown earlier]] the scalar product of a 4-Momentum vector with itself ,~~
−	~~<center><math>{\mathbf P_1}\cdot {\mathbf P^1}=E_1E_1-\vec p_1\cdot \vec p_1 =m_{1}^2</math></center> ,~~

−	~~and the length of a 4-Momentum vector composed of 4-Momentum vectors,~~
−
−	~~<center><math>{\mathbf P^2}=({\mathbf P_1}+{\mathbf P_2})^2=(E_1+E_2)^2-(\vec p_1 +\vec p_2 )^2=(m_1+m_2)^2=s</math></center>,~~
−
−	~~are invariant quantities.~~
−
−	~~It was [[DV_Calculations_of_4-momentum_components#Equal_masses \| further shown ]] that~~
−
−	~~<center><math>{\mathbf P^*}^2={\mathbf P}^2</math></center>~~
−
−
−	~~<center>''where'' <math>{\mathbf P^}=({\mathbf P_1^}+{\mathbf P_2^*})^2</math> ''represents the 4-Momentum Vector in the CM frame''</center>~~
−
−
−	~~<center> ''and'' <math>{\mathbf P}=({\mathbf P_1}+{\mathbf P_2})^2</math> ''represents the 4-Momentum Vector in the initial Lab frame''</center>~~
−
−	~~which can be expanded to~~
−
−	~~<center><math>{\mathbf P^}^2={\mathbf P^{'}}^2={\mathbf P}^2={\mathbf P^'}^2</math></center>~~
−
−
−	~~<center>''where'' <math>{\mathbf P^'}=({\mathbf P_1^'}+{\mathbf P_2^'})^2</math> ''represents the 4-Momentum Vector in the final Lab frame''</center>~~
−
−
−	~~<center>''and'' <math>{\mathbf P^{'}}=({\mathbf P_1^{'}}+{\mathbf P_2^{'*}})^2</math> ''represents the 4-Momentum Vector in the final CM frame''</center>~~

@@ Line 1: / Line 1: @@
 =Total 4-momentum=
 As was [[DV_Calculations_of_4-momentum_components#4-Momentum_Invariants | shown earlier]] the scalar product of a 4-Momentum vector with itself ,
-<center><math>{\mathbf P_1}\cdot {\mathbf P^1}=E_1E_1-\vec p_1\cdot \vec p_1 =m_{1}^2=s</math></center> ,
+<center><math>{\mathbf P_1}\cdot {\mathbf P^1}=E_1E_1-\vec p_1\cdot \vec p_1 =m_{1}^2</math></center> ,
 and the length of a 4-Momentum vector composed of 4-Momentum vectors,