Large gauge effects and the structure of amplitudes
Andrea Cristofoli (School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, EH9 3FD, U.K.); Asaad Elkhidir (Higgs Centre, School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3FD, U.K.); Anton Ilderton (Higgs Centre, School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3FD, U.K.); Donal O’Connell (Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106-4030, U.S.A., Higgs Centre, School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3FD, U.K.)
We show that large gauge transformations modify the structure of momentum conservation leading to non-vanishing three-point amplitudes in a simple toy model of a gravitational wave event. This phenomenon resolves an apparent tension between perturbative scattering amplitude computations and exact methods in field theory. The tension is resolved to all orders of perturbation theory once large gauge effects are included via a modified LSZ prescription; if they are omitted, perturbative methods only recover a subset of terms in the full non-perturbative expression. Although our results are derived in the context of specific examples, several aspects of our work have analogues in dynamical gravitational scattering processes.
