Canonical transverse photon field
= Canonical transverse photon field
{title2=$A_i^T=\sum_{r=1}^2\int\frac{d^3k}{(2\pi)^3\sqrt{2|\mathbf k|}}(\epsilon_i^{(r)}a_re^{-ikx}+\mathrm{h.c.})$}
The free transverse <photon> field is a Hermitian sum of two transverse-polarization plane-wave modes with creation and <annihilation operators>. Their standard bosonic <commutator> gives the <transverse equal-time commutator>. The normal-ordered <Hamiltonian> is a sum of positive oscillator energies.