# When can you simplify the W boson propagator

I have seen in several sources that the propagator of the $$W$$ boson is: $$\frac{- i \left( g^{\mu\nu} - \frac{P^\mu P^\nu}{m_W^2} \right)}{p^2 - m_W^2}$$ But then in some calculations (usually approximations) I have seen that only $$\frac{-i}{p^2 - m_W^2}$$ is used as the propagator. So my question is why is this allowed and when is it allowed to do this.

• Acting on a 4-vector orthogonal to p, it reproduces it times the scalar you write. Acting on a vector parallel to p it reproduces it times something else (what?). – Cosmas Zachos Feb 7 at 1:46