Radiation-gauge photon propagator (${\tilde{D}}_{ij}^F(k)=i({\delta }_{ij}-k_i{k}_j/|\mathbf{k}{|}^2)/(k^2+i0)$)

Time-ordering the canonical transverse photon field gives a propagator with numerator equal to the spatial transverse projector and denominator $k^2+i0$. Its two energy poles encode forward propagation of the positive-frequency term and backward propagation of the negative-frequency term. This is the reduced free-field propagator; it is distinct from the covariant four-potential propagator.