Variables Used in Elastic Scattering

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