Transverse projector of a vector field
= Transverse projector of a vector field
{title2=$P_T^{\mu\nu}$}
At a nonzero Euclidean <momentum> $k$, the <transverse projector of a vector field> is $P_T^{ab}=\delta^{ab}-k^ak^b/k^2$. In a Lorentzian <Minkowski metric>, its mixed-index form is $(P_T)^a{}_b=\delta^a_b-p^ap_b/p^2$, defined for $p^2\ne0$. It obeys $P_Tp=0$ and $P_T^2=P_T$. A nonzero null <four-momentum> is insufficient for this particular decomposition because the denominator vanishes.