{"paper":{"title":"Liouville term for neutrinos: Flavor structure and wave interpretation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.HE"],"primary_cat":"hep-ph","authors_text":"Georg Raffelt, G\\\"unter Sigl, Tobias Stirner","submitted_at":"2018-03-13T09:21:11Z","abstract_excerpt":"Neutrino production, absorption, transport, and flavor evolution in astrophysical environments is described by a kinetic equation $D\\varrho=-i[{\\sf H},\\varrho]+{\\cal C}[\\varrho]$. Its basic elements are generalized occupation numbers $\\varrho$, matrices in flavor space, that depend on time $t$, space $\\bf x$, and momentum $\\bf p$. The commutator expression encodes flavor conversion in terms of a matrix $\\sf H$ of oscillation frequencies, whereas ${\\cal C}[\\varrho]$ represents source and sink terms as well as collisions. The Liouville operator on the left hand side involves linear derivatives i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04693","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"}