E(2)-like little group for massless particles and neutrino polarization as a consequence of gauge invariance

The content of the isomorphism between the two-dimensional Euclidean group and the E(2)-like little group for massless particles is studied in detail. Representations of the E(2) group are explicitly constructed. The finite-dimensional representations which correspond to physical massless particles are discussed in detail, particularly for the cases of spin 1 and ½. For photons, the little-group transformation matrix is reduced to the transpose of the coordinate transformation matrix in the E(2) plane. In the case of spin-½ particles, it is shown that the polarization of neutrinos is a consequence of the requirement of gauge invariance.