Abstract
Previous analyses of asymptotic symmetries in QED have shown that the subleading soft photon theorem implies a Ward identity corresponding to a charge generating divergent large gauge transformations on the asymptotic states at null infinity. In this work, we demonstrate that the subleading soft photon theorem is equivalent to a more general Ward identity. The charge corresponding to this Ward identity can be decomposed into an electric piece and a magnetic piece. The electric piece generates the Ward identity that was previously studied, but the magnetic piece is novel, and implies the existence of an additional asymptotic “magnetic” symmetry in QED.
Highlights
Which can be massaged into a Ward identity for the S-matrix
Previous analyses of asymptotic symmetries in QED have shown that the subleading soft photon theorem implies a Ward identity corresponding to a charge generating divergent large gauge transformations on the asymptotic states at null infinity
We demonstrate that the subleading soft photon theorem is equivalent to a more general Ward identity
Summary
We introduce the notations employed in this paper (following the conventions of [10]) and review related previous work. We will focus on the scattering of massless particles, which satisfy pApA = 0 We parameterize such momenta using flat null coordinates so that pA(ω, x) = ωpA(x), pA(x) = 1 1 + x2, 2xa, 1 − x2 . One particle in- and out-states with momenta p are created from the vacuum by in (−) and out (+) creation and annihilation operators denoted by Oα(±)†(p) and Oα(±)(p), where α labels the polarization of the particle They are canonically normalized, i.e. where [·, ·} indicates an anticommutator if both operators are fermionic and a commutator otherwise. Gauge transformations that vanish at infinity map physically equivalent solutions to each other and are merely redundancies of the theory. The corresponding radiative and Coulombic fields are denoted by A(μR±) and A(μC±)
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