  In this work we extend the definition of asymptotic multi-particle states of
the $S$-matrix, beyond the direct products of one-particle states. We identify
new quantum numbers which we call pairwise helicities, or $q_{ij}$, associated
with asymptotically separated pairs of particles. These signal the appearance
of a new source of angular momentum, beyond the orbital and spin contributions.
The essence of our construction is to first treat all single particles as well
as all particle pairs independently, ultimately projecting onto the physical
states. The resulting representations reproduce the usual direct product states
for vanishing $q_{ij}$, while for vanishing spins they reproduce Zwanziger's
electric-magnetic multi-particle states. Pairwise helicity then appears as a
label for the extra little group phase for our quantum states, in addition to
their standard little group transformation. Our newly defined multi-particle
states are the correct asymptotic states for the scattering of electric and
magnetic charges, with pairwise helicity identified as $q_{ij}=e_i g_j-e_j
g_i$.
