{"paper":{"title":"Heat trace for Laplacian type operators with non-scalar symbols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.CA","math.MP","math.SP"],"primary_cat":"math.FA","authors_text":"Bruno Iochum, Thierry Masson","submitted_at":"2016-07-20T19:36:35Z","abstract_excerpt":"For an elliptic selfadjoint operator $P =-[u^{\\mu\\nu}\\partial_\\mu \\partial_\\nu +v^\\nu \\partial_\\nu +w]$ acting on a fiber bundle over a Riemannian manifold, where $u,v^\\mu,w$ are $N\\times N$-matrices, we develop a method to compute the heat-trace coefficients $a_r$ which allows to get them by a pure computational machinery. It is exemplified in dimension 4 by the value of $a_1$ written both in terms of $u,v^\\mu,w$ or diffeomorphic and gauge invariants. We also answer to the question: when is it possible to get explicit formulae for $a_r$?"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06070","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"}