# Necessity to consider the square of Four Momentum

Why do we often need to consider the square of four momentum transfer $$Q$$ in scattering experiment or particle physics/cosmology instead of just the $$Q$$ itself?

• If physical quantities were to depend on components of $Q$, the theory wouldn’t have relativistic invariance. – Prof. Legolasov May 10 at 8:24
• Do you mean why not get the length of the four-vector momentum transfer, i.e. the square root of it? the way we use m and not $m^2$ ? – anna v May 10 at 18:31

• I think the question is why $q^2$ instead of $\sqrt{q^2}$. Both are Lorentz invariant. – dukwon May 10 at 15:01