Zwanziger's pairwise little group on the celestial sphere

We generalize Zwanziger's pairwise little group to include a boost subgroup. We do so by working in the celestial sphere representation of scattering amplitudes. We propose that due to late time soft photon and graviton exchanges, matter particles in the asymptotic states in massless QED and gravity transform under the Poincare group with an additional pair of pairwise celestial representations for each pair of matter particles. We demonstrate that the massless abelian and gravitational exponentiation theorems are consistent with the proposed pairwise Poincare transformation properties. For massless QED we demonstrate that our results are consistent with the effects of the Faddeev-Kulish dressing and the abelian exponentiation theorem for celestial amplitudes found in arXiv:2012.04208. We discuss electric and magnetic charges simultaneously as it is especially natural to do so in this formalism.