Variables Used in Elastic Scattering: Difference between revisions
Jump to navigation
Jump to search
| Line 4: | Line 4: | ||
It was [[DV_Calculations_of_4-momentum_components#Equal_masses | further shown ]] that | It was [[DV_Calculations_of_4-momentum_components#Equal_masses | further shown ]] that | ||
<center><math>{\mathbf P^*}^2={\mathbf P}^2</math></center> | <center><math>{\mathbf P^*}^2={\mathbf P}^2</math></center> | ||
<center>where <math>{\mathbf P^*}</math> represents the 4-Momentum Vector in the CM frame</center> | |||
<center> and <math>{\mathbf P}</math> represents the 4-Momentum Vector in the initial Lab frame</center> | <center>''where'' <math>{\mathbf P^*}</math> ''represents the 4-Momentum Vector in the CM frame''</center> | ||
<center> ''and'' <math>{\mathbf P}</math> ''represents the 4-Momentum Vector in the initial Lab frame''</center> | |||
which can be expanded to | which can be expanded to | ||
| Line 11: | Line 12: | ||
<center><math>{\mathbf P^*}^2={\mathbf P}^2={\mathbf P^'}^2</math></center> | <center><math>{\mathbf P^*}^2={\mathbf P}^2={\mathbf P^'}^2</math></center> | ||
<center>where <math>{\mathbf P^'}</math> represents the 4-Momentum Vector in the final Lab frame</center> | <center>''where'' <math>{\mathbf P^'}</math> ''represents the 4-Momentum Vector in the final Lab frame''</center> | ||
=Mandelstam Representation= | =Mandelstam Representation= | ||
[[File:Mandelstam.png | 400 px]] | [[File:Mandelstam.png | 400 px]] | ||
Revision as of 19:25, 31 January 2016
Lorentz Invariant Quantities
As was shown earlier the scalar product of a 4-Momentum vector with itself ,[math]\displaystyle{ {\mathbf P_1}\cdot {\mathbf P^1}=E_1E_1-\vec p_1\cdot \vec p_1 =m_{1}^2=s }[/math] , and the length of a 4-Momentum vector composed of 4-Momentum vectors, [math]\displaystyle{ {\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], are invariant quantities.
It was further shown that
which can be expanded to
Mandelstam Representation
