{"work":{"id":"b25151d5-a61b-425a-bdb9-82ef3262d4d2","openalex_id":null,"doi":null,"arxiv_id":"1705.01027","raw_key":null,"title":"A Conformal Basis for Flat Space Amplitudes","authors":null,"authors_text":"S","year":2017,"venue":"hep-th","abstract":"We study solutions of the Klein-Gordon, Maxwell, and linearized Einstein equations in $\\mathbb{R}^{1,d+1}$ that transform as $d$-dimensional conformal primaries under the Lorentz group $SO(1,d+1)$. Such solutions, called conformal primary wavefunctions, are labeled by a conformal dimension $\\Delta$ and a point in $\\mathbb{R}^d$, rather than an on-shell $(d+2)$-dimensional momentum. We show that the continuum of scalar conformal primary wavefunctions on the principal continuous series $\\Delta\\in \\frac d2+ i\\mathbb{R}$ of $SO(1,d+1)$ spans a complete set of normalizable solutions to the wave equation. In the massless case, with or without spin, the transition from momentum space to conformal primary wavefunctions is implemented by a Mellin transform. As a consequence of this construction, scattering amplitudes in this basis transform covariantly under $SO(1,d+1)$ as $d$-dimensional conformal correlators.","external_url":"https://arxiv.org/abs/1705.01027","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-07-10T16:27:22.249304+00:00","pith_arxiv_id":"1705.01027","created_at":"2026-05-11T10:46:02.838156+00:00","updated_at":"2026-07-10T16:27:22.249304+00:00","title_quality_ok":true,"display_title":"A Conformal Basis for Flat Space Amplitudes","render_title":"A Conformal Basis for Flat Space Amplitudes"},"hub":{"state":{"work_id":"b25151d5-a61b-425a-bdb9-82ef3262d4d2","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":21,"external_cited_by_count":null,"distinct_field_count":2,"first_pith_cited_at":"2022-02-09T19:52:15+00:00","last_pith_cited_at":"2026-07-08T19:17:17+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-08-23T20:39:37.865379+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":5},{"context_role":"method","n":1}],"polarity_counts":[{"context_polarity":"background","n":5},{"context_polarity":"use_method","n":1}],"runs":{},"summary":{},"graph":{},"authors":[]}}