Longitudinal projector of a vector field
= Longitudinal projector of a vector field
{title2=$P_L^{\mu\nu}$}
The longitudinal projector is $P_L^{\mu\nu}=k^\mu k^\nu/k^2$. It obeys $P_T+P_L=I$, $P_TP_L=0$, and $P_T^2=P_T$, $P_L^2=P_L$.
= Longitudinal projector of a vector field
{title2=$P_L^{\mu\nu}$}
The longitudinal projector is $P_L^{\mu\nu}=k^\mu k^\nu/k^2$. It obeys $P_T+P_L=I$, $P_TP_L=0$, and $P_T^2=P_T$, $P_L^2=P_L$.