Difference between revisions of "Variables Used in Elastic Scattering"

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As was shown earlier
 
As was shown earlier
  
[[DV_Calculations_of_4-momentum_components#4-Momentum_Invariants]]
+
[[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, <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.
+
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.
  
 
=Mandelstam Representation=
 
=Mandelstam Representation=
  
 
[[File:Mandelstam.png | 400 px]]
 
[[File:Mandelstam.png | 400 px]]

Revision as of 19:12, 31 January 2016

Lorentz Invariant Quantities

As was shown earlier

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.

Mandelstam Representation

Mandelstam.png