  We extend a procedure for construction of the photon position operators with
transverse eigenvectors and commuting components [Phys. Rev. A 59, 954 (1999)]
to body rotations described by three Euler angles. The axial angle can be made
a function of the two polar angles, and different choices of the functional
dependence are analogous to different gauges of a magnetic field. Symmetries
broken by a choice of gauge are re-established by transformations within the
gauge group. The approach allows several previous proposals to be related.
Because of the coupling of the photon momentum and spin, our position operator,
like that proposed by Pryce, is a matrix that does not commute with the spin
operator. Unlike the Pryce operator, however, our operator has commuting
components, but the commutators of these components with the total angular
momentum require an extra term to rotate the matrices for each vector component
around the momentum direction. Several proofs of the nonexistence of a photon
position operator with commuting components are based on overly restrictive
premises that do not apply here.
