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We geometrically derive the explicit form of the Unitary representation ofthe Poincare group and use it to apply speed-of-light boosts to simplepolarization basis to end up with Hawton-Baylis photon position operator withcommuting components. We give explicit formulas for other photon boosteigenmodes. We investigate the underlying affine connections on the light conein momentum space and find that while Pryce connection is metricsemi-symmetric, the flat Hawton-Baylis connection is not semi-symmetric.Finally we discuss localizability of photon states localized on closed loopsand show that photon states on the circle, both unnormalized improper statesand finite norm wave packet smeared over washer-like regions are strictlylocalized with respect to Hawton-Baylis operators with commuting components andalso with respect to the noncommutative Jauch-Piron-Amrein POV measure.

The explicit form of the unitary representation of the Poincar\'e group  for vector-valued wave functions (massive and massless), with applications to  photon's localization and position operators