Search Results for « Infrared finite scattering theory »

A bstract Any non-trivial scattering with massless fields in four spacetime dimensions will generically produce an “out” state with memory which gives rise to infrared divergences in the standard S -matrix. To obtain an infrared-finite scattering theory, one must suitably include states with memory. However, except in the case of QED with massive charged particles, asymptotic states with memory that have finite energy and angular momentum have not been constructed for more general theories (e.g. massless QED, Yang-Mills and quantum gravity). To this end, we construct direct-integral representations over the “Lorentz orbit” of a given memory and classify all “orbit space representations” that have well-defined energy and angular momentum. We thereby provide an explicit construction of a large supply of physical states with memory as well as the explicit action of the BMS charges all states. The construction of such states is a key step toward the formulation of an infrared-finite scattering theory. While we primarily focus on the quantum gravitational case, we outline how the methods presented in this paper can be applied to obtain representations of the Poincaré group with memory for more general quantum field theories.

Any nontrivial scattering with massless fields in four spacetime dimensions will generically produce an out-state with memory. Scattering with any massless fields violates the standard assumption of asymptotic completeness—that all “in” and “out” states lie in the standard (zero-memory) Fock space—and therefore leads to infrared divergences in the standard S -matrix amplitudes. In this paper, we define an infrared finite scattering theory which assumes only (1) the existence of in-/out-algebras and (2) that Heisenberg evolution is an automorphism of these algebras. The resulting “superscattering” map $ allows for transitions between different in/out memory states and agrees with the standard S matrix when it is defined. We construct $ amplitudes by defining (3) a “generalized asymptotic completeness” which accommodates states with memory in the space of asymptotic states and (4) a complete basis of improper states that generalize the usual n -particle momentum basis to account for states with memory. Using only general properties of $ , we prove an analog of the Weinberg soft theorems in quantum gravity and QED which imply that all $ amplitudes are well defined in the infrared. We comment on how one must generalize this framework to consider $ amplitudes for theories with collinear divergences (e.g., massless QED and Yang-Mills theories). Published by the American Physical Society 2024