{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"b156a5277ee1b67ac68a99cb60fd000ab1548be23fadd66756b9cc1d09da5399","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"193f97a9a76455de233ac08c2597c9032e80c358dfcadca9dde0ab920bc4366b","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.yang-mills.nontrivial-4d-qft","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Build, with full proof, one quantum field theory in 3+1 dimensions in which particles actually scatter off each other. Every rigorous example so far is either free (no interaction) or lives in fewer dimensions.","posed_since":"","precise":"Construct a quantum field theory on $R^{(1,3)}$ satisfying the Wightman axioms (or Euclidean Osterwalder-Schrader axioms on $R^4$) whose truncated correlation functions are not all zero, i.e. a non-Gaussian theory with nontrivial scattering. Lattice $\\phi^4$ and Ising models in $d = 4$ give only Gaussian scaling limits, so candidates are asymptotically free theories such as Yang-Mills. Answer: an explicit construction with proof of the axioms and of non-Gaussianity.","problem_ref":null,"references":"","settled_by":"A refereed construction of one non-Gaussian Wightman or Osterwalder-Schrader theory in four dimensions.","status_note":"Aizenman and Duminil-Copin (Annals of Mathematics, 2021) proved that scaling limits of critical $4\\mathrm{D}$ Ising and lattice $\\phi^{4}$ models are Gaussian, removing the simplest candidate.","title":"Construct any interacting quantum field theory in four spacetime dimensions","topic_ref":"c1a7c5336cf6e262c1ec8a96010ceec0183209142167af7077f763d0eba2c1d0"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"4910c35b91df40c4b4ae6c3b2c07380b680f81b93f76b71f30889c5407bdc3c1","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"b7c3baa5cb2b6e187f25b8623caeed69fa6fda6bc37137d041b46ac99689a59f","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"AuTD-bNGYPpRVtRbRHp0YMH3UCBH807gT8x6obtM3ytyopFwBNTS8AvpKzkDhzJaVMVm9T0wnYE7tZ5DA7PGBA"},"schema":"pubphys.envelope/1"},"record_hash":"4910c35b91df40c4b4ae6c3b2c07380b680f81b93f76b71f30889c5407bdc3c1","leaf_index":1661}