Interacting Fields at Spatial Infinity

We study the properties of massive fields extrapolated to the blowup of spatial infinity (î⁰), extending the program initiated in arXiv:2207.06406. In the free theory, we find an explicit representation of boundary two-point functions and boundary to bulk two-point functions, and also present an HKLL-type reconstruction formula for local bulk operators in terms of smeared boundary operators. We study interacting Wightman correlators and find that, generically, interacting massive fields decay slower than free fields as one approaches î⁰. We propose that meaningful correlators at î⁰ can be obtained through an LSZ-like prescription that isolates the on-shell part of bulk Wightman correlators before extrapolating them to î⁰. We show that a natural basis for operators at î⁰, defined via this prescription, is given by the average of "in" and "out" operators defined at i⁻ and i⁺ respectively. Therefore, correlators at î⁰ and cross correlators between î⁰, i⁻ and i⁺ can be represented within the class of asymptotic observables studied by Caron-Huot et al. in arXiv:2308.02125. We present several sample calculations.