{"id":"openai-math/Scale-and-conformal-symmetry-in-four-dimensional-operational-quantum-field-theory","pdf":"https://github.com/openai/math/blob/main/preprints/Scale-and-conformal-symmetry-in-four-dimensional-operational-quantum-field-theory-September-26-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Scale-and-conformal-symmetry-in-four-dimensional-operational-quantum-field-theory-September-26-2026","tags":["quantum-field-theory","conformal-symmetry","operator-algebras"],"score":0,"title":"Scale and conformal symmetry in four-dimensional operational quantum field theory","domain":"Mathematical physics","family":"282","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"We prove that scale symmetry implies local conformal symmetry for a class of four-dimensional unitary, positive-energy quantum field theories with a Poincaré- and scale-invariant vacuum. The class has a discrete, bounded-below spectrum of scaling dimensions with finite multiplicities, and each original field has finite scaling support. The original fields and their adjoints have compatible affiliated realizations in a causally commuting bounded local net, and a physical local dilatation current generates scale transformations through its local Ward identities. The operational framework…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-26","reactions":{},"formalized":false,"family_title":"From scale symmetry to local conformal symmetry in four-dimensional QFT"}