= Transverse and longitudinal momentum projectors
{title2=$P_L{}^\mu{}_\nu=k^\mu k_\nu/k^2,\quad P_T=I-P_L$}
At non-null <four-momentum>, these complementary <projectors> satisfy $P_L^2=P_L$, $P_T^2=P_T$ and $P_LP_T=0$. The <gauge-fixed Maxwell kinetic operator> is $-k^2(P_T+\xi^{-1}P_L)$; its inverse gives propagator $-i(P_T+\xi P_L)/k^2$. Transversality here removes one four-dimensional longitudinal direction, leaving rank three; it does not by itself project onto the two physical photon polarizations. The pole requires the <Feynman i-epsilon prescription>.
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