{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"18be95caac0737f95732ca230aae6d7bef3ef1d10bf57d11a79f1cb0b6b44d2a","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"3095154b6600a9480e5951ead13727c5d63d41194a7af1c89e71f24a8365d40a","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"qft.massless-bootstrap.ir-safe-smatrix","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"In four dimensions, every scattering of charged particles or gravitons emits unlimited numbers of very low-energy photons or gravitons, so the usual scattering amplitude is ill-defined. A replacement object with the properties bootstrap methods need has not been established.","posed_since":"","precise":"For 4D theories with massless gauge bosons or gravitons, define nonperturbatively asymptotic observables (dressed amplitudes, Faddeev-Kulish states, or inclusive cross sections) that are infrared finite and obey unitarity, analyticity and crossing in a form usable for numerical bootstrap. An answer is such a definition with proofs of these properties, or a demonstration that one of them must fail.","problem_ref":null,"references":"","settled_by":"A definition with nonperturbative proofs of unitarity, analyticity and crossing, used in a working numerical bootstrap.","status_note":"Generalized crossing relations between different asymptotic observables were proven at tree level in 2023 (Caron-Huot, Giroux, Hannesdottir, Mizera, arXiv:2310.12199).","title":"Bootstrap-ready scattering observables with soft photons and gravitons","topic_ref":"ec37b6151c82884c89bcd0edd8abd842fda27798c1918aa964b247ee16f12213"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"ca81236ea6cf87bdfb0d6a5afbf46810bf7277857910388b7bc7a8792b172ae6","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"09f1b83b3563edcf2d74fad08fc88437f714f803a88b15f924d1f6a63736118a","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"MnMb7B1qiJ1TIrfeG9q6WWeOjSVUENYst_f_qa_C_h0TKPKeYfliIX94H5IVKFIckukNiaPw-KNQhaT83-jVBQ"},"schema":"pubphys.envelope/1"},"record_hash":"ca81236ea6cf87bdfb0d6a5afbf46810bf7277857910388b7bc7a8792b172ae6","leaf_index":1923}