Abstract
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 Poincaré 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 Poincaré 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.
Highlights
Theory of Zwanziger’s pairwise little group [8], our work generalizes Zwanziger’s pairwise little group to include a boost subgroup
We propose that due to late time soft photon and graviton exchanges, matter particles in the asymptotic states in massless quantum electrodynamics (QED) and gravity transform under the Poincaré 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 Poincaré transformation properties
Summary
The interaction between an electric-magnetic charged pair leads to a quantized amount of angular momentum to be stored in the electromagnetic field at asymptotic times. In order to claim that the states at t → ±∞ transform as free particle representations one requires that V (t), W (t) effectively vanish at asymptotic times In this context, we can say that an interaction picture operator effectively vanishes at asymptotic times if its late time matrix elements between smooth superpositions of H0 eigenstates |ψα , |ψβ exhibits no poles of the form. In theories where massless particles can be exchanged this condition is generically not met and the asymptotic states do not transform as free particle representations. We can trivially take the late time limit and observe that lim t→∞ This suggests that the asymptotic boost operator does not coincide with the free field theory boost operator, and that the asymptotic states do not transform as free particle representations under boosts. What we find in this paper is that Zwanziger’s procedure, when applied to celestial states, suggests that the net effect of late time interactions for massless charged particles is to add to each pair of massless charged particles a pair of celestial states with conformal dimension ij ei ej 4π2 log ΛIR
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