Geometrical interpretation of the photon position operator with commuting components

It is shown that the photon position operator \^{}P{X} with commuting components can be written in the momentum representation as \^{}P{X}=i \^{}P{D}, where \^{}P{D} is a flat connection in the tangent bundle T (R^3 (0, 0, {k₃) R^3: k₃0}) over R^3 (0, 0, {k₃) R^3: k₃0} equipped with the Cartesian structure. Moreover, \^{}P{D} is such that the tangent 2-planes orthogonal to the momentum are propagated parallel with respect to \^{}P{D} and also \^{}P{D} is an anti-Hermitian (i. e. , \^{}P{X} is Hermitian) operator with respect to the scalar product | { \^{}H}^-2s|. The eigenfunctions ₏ₗ (Px) of the position operator \^{}P{X} are found.