Variables Used in Elastic Scattering

Lorentz Invariant Quantities

As was shown earlier

DV_Calculations_of_4-momentum_components#4-Momentum_Invariants

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, [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