  A general form of the photon position operator with commuting components
fulfilling some natural axioms is obtained. This operator commutes with the
photon helicity operator, is Hermitian with respect to the Bialynicki-Birula
scalar product and defined up to a unitary transformation preserving the
transversality condition. It is shown that, using the procedure analogous to
the one introduced by T. T. Wu and C. N. Yang for the case of the Dirac
magnetic monopole, the photon position operator can be defined by a flat
connection in some trivial vector bundle over $\mathbb{R}^3 \setminus
\{(0,0,0)\}$. This observation enables us to reformulate quantum mechanics of
a~single photon on $(\mathbb{R}^{3} \setminus \{(0,0,0)\}) \times
\mathbb{C}^2$.

Quantum Physics