{"paper":{"title":"Dirac operator on spinors and diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Giacomo Dossena, Ludwik Dabrowski","submitted_at":"2012-09-10T15:06:59Z","abstract_excerpt":"The issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold $M$, to each spin structure $\\sigma$ and Riemannian metric $g$ there is associated a space $S_{\\sigma, g}$ of spinor fields on $M$ and a Hilbert space $\\HH_{\\sigma, g}= L^2(S_{\\sigma, g},\\vol{M}{g})$ of $L^2$-spinors of $S_{\\sigma, g}$. The group $\\diff{M}$ of orientation-preserving diffeomorphisms of $M$ acts both on $g$ (by pullback) and on $[\\sigma]$ (by a suitably defined pullback $f^*\\sigma$). Any $f\\in \\diff{M}$ lifts in exactly two ways to a unitary operator $U$ from $\\HH_{\\sigma, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2021","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"}