  Recently (Phys. Rev. Lett. 114 (2015), 210402) the influence of the so called
"Wigner translations" (more generally-Lorentz trans- formations) on circularly
polarized Gaussian packets ( providing the solution to Maxwell equations in
paraxial approximation) has been studied. It appears that, within this
approximation, the Wigner trans- lations have an efect of shifting the wave
packet trajectory parallel to itself by an amount proportional to the photon
helicity. It has been suggested that this shift may result from specific
properties of the algebra of Poincare generators for massless particles. In the
present letter we describe the general relation between transformation proper-
ties of electromagnetic field on quantum and classical levels. It allows for a
straightforward derivation of the helicity-dependent transforma- tion rules. We
present also an elementary derivation of the formula for sideways shift based
on classical Maxwell theory. Some comments are made concerning the
generalization to higher helicities and the relation to the coordinate operator
defined long time ago by Pryce.
