Infrared finite scattering theory: Amplitudes and soft theorems

Understand

Any non-trivial 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 (IR) 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.