{"paper":{"title":"Comment on higher derivative Lagrangians in relativistic theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Mathieu Beau (STP-DIAS)","submitted_at":"2013-05-24T14:50:40Z","abstract_excerpt":"We discuss the consequences of higher derivative Lagrangians of the form $\\alpha_1 A_{\\mu}(x)\\dot{x}^\\mu$, $\\alpha_2 G_{\\mu}(x)\\ddot{x}^\\mu$, $\\alpha_3 B_{\\mu}(x)\\dddot{x}^\\mu$, $\\alpha_4 K_{\\mu}(x)\\ddddot{x}^\\mu$, $\\cdots$, $U_{(n)\\mu}(x)x^{(n)\\mu}$ in relativistic theory. After establishing the equations of the motion of particles in these fields, we introduce the concept of the generalized induction principle assuming the coupling between the higher fields $U_{(n),\\mu}(x),\\ n\\geq1$ with the higher currents $j^{(n)\\mu}=\\rho(x)x^{(n)\\mu}$, where $\\rho(x)$ is the spatial density of mass or of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5759","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"}