{"paper":{"title":"Sp(2,$\\mathbb{Z}$) invariant Wigner function on even dimensional vector space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Akihisa Hayashi, Minoru Horibe, Takaaki Hashimoto","submitted_at":"2013-01-31T08:24:30Z","abstract_excerpt":"We construct the quasi probability distribution $W(p,q)$ on even dimensional vector space with marginality and invariance under the transformation induced by projective representation of the group ${\\rm Sp}(2,\\mathbb{Z})$ whose elements correspond to linear canonical transformation.\n  On even dimensional vector space, non-existence of such a quasi probability distribution whose arguments take physical values was shown in our previous paper(Phys.Rev.A{\\bf 65} 032105(2002)). For this reason we study a quasi probability distribution $W(p,q)$ whose arguments $q$ and $p$ take not only $N$ physical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7541","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"}