{"paper":{"title":"Fock representations of $Q$-deformed commutation relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Eugene Lytvynov, Janusz Wysocza\\'nski, Marek Bo\\.zejko","submitted_at":"2016-03-08T09:39:05Z","abstract_excerpt":"We consider Fock representations of the $Q$-deformed commutation relations $$\\partial_s\\partial^\\dag_t=Q(s,t)\\partial_t^\\dag\\partial_s+\\delta(s,t), \\quad s,t\\in T.$$ Here\n  $T:=\\mathbb R^d$ (or more generally $T$ is a locally compact Polish space), the function $Q:T^2\\to \\mathbb C$ satisfies $|Q(s,t)|\\le1$ and $Q(s,t)=\\overline{Q(t,s)}$, and $$\\int_{T^2}h(s)g(t)\\delta(s,t)\\,\\sigma(ds)\\sigma(dt):=\\int_T h(t)g(t)\\,\\sigma(dt),$$\n  $\\sigma$ being a fixed reference measure on $T$. In the case where $|Q(s,t)|\\equiv 1$, the $Q$-deformed commutation relations describe a generalized statistics studied "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03075","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"}