{"paper":{"title":"Extension of distributions, scalings and renormalization of QFT on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Nguyen Viet Dang","submitted_at":"2014-11-13T19:25:13Z","abstract_excerpt":"Let $M$ be a smooth manifold and $X\\subset M$ a closed subset of $M$. In this paper, we introduce a natural condition of \\emph{moderate growth} along $X$ for a distribution $t$ in $\\mathcal{D}^\\prime(M\\setminus X)$ and prove that this condition is equivalent to the existence of an extension of $t$ in $\\mathcal{D}^\\prime(M)$ generalizing some previous results of Meyer and Brunetti--Fredenhagen. When $X$ is a closed submanifold of $M$, we show that the concept of distributions with moderate growth coincides with weakly homogeneous distributions of Meyer. Then we renormalize products of distribut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3670","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"}