Internal space-time symmetries of massive and massless particles and their unification

Abstract

It is noted that the internal space-time symmetries of relativistic particles are dictated by Wigner's little groups. The symmetry of massive particles is like the three-dimensional rotation group, while the symmetry of massless particles is locally isomorphic to the two-dimensional Euclidean group. It is noted also that, while the rotational degree of freedom for a massless particle leads to its helicity, the two translational degrees of freedom correspond to its gauge degrees of freedom. It is shown that the E(2)-like symmetry of of massless particles can be obtained as an infinite-momentum and/or zero-mass limit of the O(3)-like symmetry of massive particles. This mechanism is illustrated in terms of a sphere elongating into a cylinder. In this way, the helicity degree of freedom remains invariant under the Lorentz boost, but the transverse rotational degrees of freedom become contracted into the gauge degree of freedom.

Classical aspects of lightlike dimensional reduction

“…Note that if τ = 0 and R a b = I a b , the parameter λ changes while τ and ǫ do not. This fact led some authors [12,16,1,30] to the conclusion that the generators W a generate gauge transformations instead of Galilean boosts.…”