  It is shown that the photon position operator $\hat{\vec{X}}$ with commuting
components can be written in the momentum representation as $\hat{\vec{X}}=i
\hat{\vec{D}}$, where $\hat{\vec{D}}$ is a flat connection in the tangent
bundle $T(\mathbb{R}^3 \setminus \{ (0,0,k_3) \in \mathbb{R}^3 : k_3 \geq 0\})$
over $\mathbb{R}^3 \setminus \{ (0,0,k_3) \in \mathbb{R}^3 : k_3 \geq 0\}$
equipped with the Cartesian structure. Moreover, $\hat{\vec{D}}$ is such that
the tangent $2$-planes orthogonal to the momentum are parallelly propagated
with respect to $\hat{\vec{D}}$ and, also, $\hat{\vec{D}}$ is an anti-Hermitian
operator with respect to the scalar product $\langle \mathbf{\Psi} |
\hat{H}^{-2s} |\mathbf{\Phi} \rangle$. The eigenfunctions
$\mathbf{\Psi}_{\vec{X}} (\vec{x})$ of the position operator $\hat{\vec{X}}$
are found.
