{"paper":{"title":"Two-point one-dimensional $\\delta$-$\\delta^\\prime$ interactions: non-abelian addition law and decoupling limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"J. Mateos Guilarte, J. M. Munoz-Castaneda, L. M. Nieto, M. Gadella","submitted_at":"2015-05-17T06:03:25Z","abstract_excerpt":"In this contribution to the study of one dimensional point potentials, we prove that if we take the limit $q\\to 0$ on a potential of the type $v_0\\delta({y})+{2}v_1\\delta'({y})+w_0\\delta({y}-q)+ {2} w_1\\delta'({y}-q)$, we obtain a new point potential of the type ${u_0} \\delta({y})+{2 u_1} \\delta'({y})$, when $ u_0$ and $ u_1$ are related to $v_0$, $v_1$, $w_0$ and $w_1$ by a law having the structure of a group. This is the Borel subgroup of $SL_2({\\mathbb R})$. We also obtain the non-abelian addition law from the scattering data. The spectra of the Hamiltonian in the exceptional cases emerging"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04359","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"}