Massless contraction of massive particles in the infinite boost limit

Abstract

Massless particles, defined through Wigner's induced representations of the Poincaré group, are obtained as a limit of infinitely boosted massive particles wherein the massive little group undergoes an Inönü--Wigner contraction to the massless one. It is demonstrated that the spin-$s$ multiplet of a massive representation re-organizes into the direct sum of massless particles with helicities in the range $[-s,s]$. This group theoretic result is the Hilbert space counterpart of the Stückelberg formulation of massive fields of spin $s$ in the high-energy limit, where the Stückelberg fields become independent massless fields of spins $s'\leq s$ in integer steps. It therefore also provides the kinematic setting of the Goldstone equivalence theorem.