Difference between revisions of "Variables Used in Elastic Scattering"

From New IAC Wiki
Jump to navigation Jump to search
(Blanked the page)
 
(55 intermediate revisions by the same user not shown)
Line 1: Line 1:
=Lorentz Invariant Quantities=
 
As was [[DV_Calculations_of_4-momentum_components#4-Momentum_Invariants | shown earlier]] the scalar product of a 4-Momentum vector with itself ,<math>{\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>{\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 [[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^*}</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
 
 
<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>
 
 
=Mandelstam Representation=
 
 
[[File:Mandelstam.png | 400 px]]
 

Latest revision as of 19:10, 1 June 2017