{"paper":{"title":"Volume elements of spacetime and a quartet of scalar fields","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Alfredo Mac\\'ias, Frank Gronwald, Friedrich W. Hehl, Uwe Muench","submitted_at":"1997-12-15T18:52:04Z","abstract_excerpt":"Starting with a `bare' 4-dimensional differential manifold as a model of spacetime, we discuss the options one has for defining a volume element which can be used for physical theories. We show that one has to prescribe a scalar density \\sigma. Whereas conventionally \\sqrt{|\\det g_{ij}|} is used for that purpose, with g_{ij} as the components of the metric, we point out other possibilities, namely \\sigma as a `dilaton' field or as a derived quantity from either a linear connection or a quartet of scalar fields, as suggested by Guendelman and Kaganovich."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9712063","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"}