Timelike photon polarization (source code)

= Timelike photon polarization
{title2=$\epsilon^{0\mu}=(1,0,0,0)$}

A timelike basis polarization in covariant photon quantization has positive <Minkowski metric> squared length, conventionally $\epsilon^{0\mu}=(1,\mathbf0)$ with signature $(+,-,-,-)$. It is distinct from the spatial <longitudinal polarization> $\epsilon^{3\mu}=(0,\widehat{\mathbf p})$. The extra minus sign in the covariant oscillator <commutator> makes its one-photon state a <negative-norm photon state>. Neither this temporal polarization nor an isolated longitudinal photon survives the <Gupta-Bleuler null-state quotient>.