The localization of photons
Abstract
We propose a position operator for the photon. The components commute and commute with helicity, and the two operators form a complete set of commuting observables. However, the simultaneous eigenvectors of this position operator and helicity do not rotate locally. For a normalized wavepacket state vector, the positionhelicity amplitudes give a complete characterization of the physical properties of the state vector, yet their modulisquared have rotation properties that do not have a simple interpretation. Thus we call these pseudoamplitudes. We show that there is a regime of wavepacket state vectors, those with a small fractional spread around an average momentum, where the positionhelicity probability pseudodensities rotate very nearly locally as scalar functions. This is just the regime that is needed to describe a scattering experiment involving photons. We consider other measures of localization for the photon, including those proposed by other authors. It is important to note that exactly the same problems arise if we try to characterize the state vector of a massive particle with spin by position and helicity. The problems are not the result of the masslessness of the photon but arise because of its limited helicity spectrum.
 Publication:

arXiv eprints
 Pub Date:
 August 2019
 arXiv:
 arXiv:1909.00158
 Bibcode:
 2019arXiv190900158H
 Keywords:

 Quantum Physics
 EPrint:
 16 pages, 1 figure, some revisions in Version 2