Variables Used in Elastic Scattering: Difference between revisions
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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
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.
Mandelstam Representation
