{"paper":{"title":"Spectral analysis of an abstract pair interaction model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Daiju Funakawa, Keisuke Asahara","submitted_at":"2018-07-23T02:36:13Z","abstract_excerpt":"We consider an abstract pair-interaction model in quantum field theory with a coupling constant $\\lambda\\in {\\mathbb R}$ and analyze the Hamiltonian $H(\\lambda)$ of the model. In the massive case, there exist constants $\\lambda_{\\rm c}<0$ and $\\lambda_{{\\rm c},0}<\\lambda_{\\rm c}$ such that, for each $\\lambda \\in (\\lambda_{{\\rm c},0},\\lambda_{\\rm c})\\cup (\\lambda_{\\rm c},\\infty)$, $H(\\lambda)$ is diagonalized by a proper Bogoliubov transformation, so that the spectrum of $H(\\lambda)$ is explicitly identified, where the spectrum of $H(\\lambda)$ for $\\lambda>\\lambda_{\\rm c}$ is different from tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08408","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"}