{"paper":{"title":"From Quantum Mechanics to Quantum Field Theory: The Hopf route","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Allan I. Solomon (LPTMC), Andrzej Horzela (IFJ-PAN - Polish Academy of Sciences), G\\'erard Henry Edmond Duchamp (LIPN), Karol A. Penson (LPTMC), Pawel Blasiak (IFJ-PAN - Polish Academy of Sciences)","submitted_at":"2010-11-02T06:53:56Z","abstract_excerpt":"We show that the combinatorial numbers known as {\\em Bell numbers} are generic in quantum physics. This is because they arise in the procedure known as {\\em Normal ordering} of bosons, a procedure which is involved in the evaluation of quantum functions such as the canonical partition function of quantum statistical physics, {\\it inter alia}. In fact, we shall show that an evaluation of the non-interacting partition function for a single boson system is identical to integrating the {\\em exponential generating function} of the Bell numbers, which is a device for encapsulating a combinatorial se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0524","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"}