{"paper":{"title":"Construction of the \\Phi^4_4-quantum field theory on noncommutative Moyal space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Harald Grosse (Vienna), Raimar Wulkenhaar (M\\\"unster)","submitted_at":"2014-02-05T14:06:02Z","abstract_excerpt":"We review our recent construction of the $\\phi^4$-model on four-dimensional Moyal space. A milestone is the exact solution of the quartic matrix model $Z[E,J]=\\int d\\Phi \\exp(tr(J\\Phi- E\\Phi^2 -(\\lambda/4) \\Phi^4))$ in terms of the solution of a non-linear equation for the 2-point function and the eigenvalues of $E$. The $\\beta$-function vanishes identically. For the Moyal model, the theory of Carleman type singular integral equations reduces the construction to a fixed point problem. Its numerical solution reveals a second-order phase transition at $\\lambda_c\\approx-0.396$ and a phase transit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1041","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}