{"paper":{"title":"Heat asymptotics for nonminimal Laplace type operators and application to noncommutative tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.OA"],"primary_cat":"math.DG","authors_text":"Bruno Iochum, Thierry Masson","submitted_at":"2017-07-30T19:13:51Z","abstract_excerpt":"Let $P$ be a Laplace type operator acting on a smooth hermitean vector bundle $V$ of fiber $\\mathbb{C}^N$ over a compact Riemannian manifold given locally by $P= - [g^{\\mu\\nu} u(x)\\partial_\\mu\\partial_\\nu + v^\\nu(x)\\partial_\\nu + w(x)]$ where $u,\\,v^\\nu,\\,w$ are $M_N(\\mathbb{C})$-valued functions with $u(x)$ positive and invertible. For any $a \\in \\Gamma(\\text{End}(V))$, we consider the asymptotics $\\text{Tr} (a e^{-tP}) \\underset{t \\downarrow 0^+}{\\sim} \\,\\sum_{r=0}^\\infty a_r(a, P)\\,t^{(r-d)/2}$ where the coefficients $a_r(a, P)$ can be written locally as $a_r(a, P)(x) = \\text{tr}[a(x) \\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09657","kind":"arxiv","version":2},"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"}