{"paper":{"title":"Invariant PDEs of Conformal Galilei Algebra as deformations: cryptohermiticity and contractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"F. Toppan, N. Aizawa, Z. Kuznetsova","submitted_at":"2015-06-29T02:08:20Z","abstract_excerpt":"We investigate the general class of second-order PDEs, invariant under the $d=1$ $\\ell=\\frac{1}{2}+{\\mathbb N}_0$ centrally extended Conformal Galilei Algebras, pointing out that they are deformations of decoupled systems. For $\\ell=\\frac{3}{2}$ the unique deformation parameter $\\gamma$ belongs to the fundamental domain $\\gamma\\in ]0,+\\infty[$. We show that, for any $\\gamma\\neq 0$, invariant PDEs with discrete spectrum (either bounded or unbounded) induce cryptohermitian operators possessing the same spectrum as two decoupled oscillators, provided that their frequencies are in the special rati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08488","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"}