--------------------------- Helicity and Hopf fibration --------------------------- There is a relation between massless (helicity) representations of the Poincare group and the Hopf fibration, a nontrivial principal fiber bundle on the 3-sphere, with the 2-sphere as basis manifold. See Section 4 in http://arxiv.org/pdf/0908.1205 and the paper [7] by Urbantke quoted there. Thus there are interesting topological issues in the massless case. Also related is Section 2.4 in http://arxiv.org/pdf/math-ph/0303031 It would be nice to have a short and elementary presentation of this connection. For a presentation in German, see http://www.itp.uni-hannover.de/~dragon/hel1.pdf (The position operator for photons presented there has a nonstandard behavior under rotations of the Poincare group: The probability density |psi(x)|^2 of position x in the position representation gives probabilites for x lying in the unit sphere that depends on the orientation of the observer frame.)