Transverse equal-time commutator
= Transverse equal-time commutator
{title2=$[A_i^T(t,\mathbf x),\Pi^{Tj}(t,\mathbf y)]=i\delta^T_{ij}(\mathbf x-\mathbf y)$}
The reduced <canonical commutation relation> for a transverse field uses a transverse delta function instead of an unconstrained componentwise delta. Its Fourier transform is the spatial transverse projector. It can be derived from the two-polarization oscillator expansion or from the <Dirac bracket> after <gauge fixing>.