= Transverse one-photon physical quotient
{title2=$c_3=-c_0,\qquad\|\chi\|^2=|c_1|^2+|c_2|^2$}
Choose a temporal <polarization vector>, two transverse <polarization vectors> and a spatial longitudinal <polarization vector>. The <Gupta-Bleuler quantization> condition is $(a^0-a^3)|\chi\rangle=0$. Applied to $\sum_\lambda c_\lambda a^{\lambda\dagger}|0\rangle$, it gives $c_3=-c_0$. The remaining temporal-longitudinal excitation $a^{0\dagger}-a^{3\dagger}$ has zero norm and is orthogonal to every constrained state. Its field wavefunction is proportional to the null <four-momentum>, hence is pure gauge. Quotienting this direction leaves the two positive transverse <photon> states. Use <wave packets> or a box normalization to avoid treating continuum momentum eigenstates as normalizable vectors.
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