{"paper":{"title":"On a Generalisation of the Poincare-Cartan Form to Classical Field Theory","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"math.DG","authors_text":"Dan Radu Grigore","submitted_at":"1998-01-15T12:27:54Z","abstract_excerpt":"We present here a possible generalisation of the Poincar\\'e-Cartan form in classical field theory in the most general case: arbitrary dimension, arbitrary order of the theory and in the absence of a fibre bundle structure. We use for the kinematical description of the system the $(r,n)$-Grassmann manifold associated to a given manifold $X$, i.e. the manifold of $r$-contact elements of $n$-dimensional submanifolds of $X$. The idea is to define globally a $n+1$ form on this Grassmann manifold, more precisely its class with respect to a certain subspace and to write it locally as the exterior der"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9801073","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"}