We study the properties of massive fields extrapolated to the blowup of spatial infinity (${\widehat{i}}^0$), extending the program initiated by Laddha et al. [Squinting at massive fields from infinity, 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 a Hamilton–Kabat–Lifschytz–Lowe (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 ${\widehat{i}}^0$. We propose that meaningful correlators at ${\widehat{i}}^0$ can be obtained through a Lehmann–Symanzik–Zimmermann (LSZ)-like prescription that isolates the on-shell part of bulk Wightman correlators before extrapolating them to ${\widehat{i}}^0$. We show that a natural basis for operators at ${\widehat{i}}^0$, defined via this prescription, is given by the average of “in” and “out” operators defined at $i^{-}$ and $i^{+}$, respectively. Therefore, correlators at ${\widehat{i}}^0$ and cross-correlators between ${\widehat{i}}^0$, $i^{-}$, and $i^{+}$ can be represented within the class of asymptotic observables studied by Caron-Huot et al. [What can be measured asymptotically?, J. High Energy Phys. 01 (2024) 139]. We present several sample calculations.

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• Perturbation theory
• Quantum field theory
• Scattering amplitudes