Completing Multiparticle Representations of the Poincare Group

Abstract

We extend the definition of asymptotic multiparticle states of the S-matrix beyond the tensor products of one-particle states. We identify new quantum numbers called pairwise helicities, or q(ij), associated with asymptotically separated pairs of particles. We first treat all single particles and particle pairs independently, allowing us to generalize the Wigner construction, and ultimately projecting onto the physical states. Our states reduce to tensor product states for vanishing q(ij), while for vanishing spins they reproduce Zwanziger's scalar dyon states. This construction yields the correct asymptotic states for the scattering of electric and magnetic charges, with pairwise helicity identified as q(ij) = e(i)g(j) - e(j)g(i).