{"paper":{"title":"${\\mathbb Z}_2\\times {\\mathbb Z}_2$-graded Lie Symmetries of the L\\'evy-Leblond Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"F. Toppan, H. Tanaka, N. Aizawa, Z. Kuznetsova","submitted_at":"2016-09-27T00:00:31Z","abstract_excerpt":"The first-order differential L\\'evy-Leblond equations (LLE's) are the non-relativistic analogs of the Dirac equation, being square roots of ($1+d$)-dimensional Schr\\\"odinger or heat equations. Just like the Dirac equation, the LLE's possess a natural supersymmetry. In previous works it was shown that non supersymmetric PDE's (notably, the Schr\\\"odinger equations for free particles or in the presence of a harmonic potential), admit a natural ${\\mathbb Z}_2$-graded Lie symmetry. In this paper we show that, for a certain class of supersymmetric PDE's, a natural ${\\mathbb Z}_2\\times{\\mathbb Z}_2$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08224","kind":"arxiv","version":3},"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"}