{"created":"2023-07-27T06:58:28.902985+00:00","id":56995,"links":{},"metadata":{"_buckets":{"deposit":"fa56cbf3-0baa-4edd-a9de-ec18c033d7b2"},"_deposit":{"created_by":18,"id":"56995","owners":[18],"pid":{"revision_id":0,"type":"depid","value":"56995"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00056995","sets":["2812:2813:2827"]},"author_link":["15115","2364"],"item_9_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2008-05-26","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"2p.","bibliographicVolumeNumber":"2004 – 2006","bibliographic_titles":[{"bibliographic_title":"平成18(2006)年度 科学研究費補助金 基盤研究(B) 研究成果報告書概要"},{"bibliographic_title":"2006 Fiscal Year Final Research Report Summary","bibliographic_titleLang":"en"}]}]},"item_9_creator_33":{"attribute_name":"著者別表示","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{}],"nameIdentifiers":[{},{},{}]}]},"item_9_description_21":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"本研究は,研究者代表者一瀬が研究分担者田村英男,田村博志,海外研究協力者V.A.Zagrebnovとの共著の2編の論文で2001年Commun.Math.Phys..誌に発表した作用素ノルム自己共役Trotter積公式に関する結果を更に発展させるべく始められた。経路積分を念頭に,シュレーディンガー作用素論における例や応用を参考にしながら,Trotter積公式及び関連する問題に関して,次の成果が得られた。\n(1)作用素ノルムTrotter積公式の更なる展開:一般には作用素ノルムTrotter積公式は,2つの自己共役作用素の2次形式和の場合には成立しない。一瀬は,H.Neidhardt及びV.A.Zagrebnovとの共著論文で,ある条件の下に成立することをJ. Functional Analysis(2004)誌で証明した。この条件が改良されるか、今後の問題である。作用素ノルムユニタリTrotter積公式は成立しないと思い込んでいたが,一瀬は田村英男との共同研究で,ディラック作用素と相対論的シュレーディンガー作用素に対して非自明なスカラー・ポテンシャルの場合に,それが成立することを発見Lett.Math.Phys.(2004)誌に発表した。\n(2)経路積分の問題,及び,Trotter積の積分核の収束の問題:藤原大輔は大きな次元での振動積分の停留位相法の剰余項評価を精密にすることに成功,それを用いてFeynman経路積分の準古典近似の第2項の形を決めることができた。成果を2006年J.Math.Soc.Japan誌にこの成果を発表した。Trotter積公式は経路積分的に言えば,経路を不連続な時間分割経路による近似を与えており,作用素ノルム自己共役Trotter積公式の近似の良さから,積分核の各点収束も言えているのではないかという問題を田村英男と共に考えた。実際,予想通りであることをComm.PDE(2004)とJ.Reine Angew, Math.(2006)の2誌でそれを確かめた。\n(3)ゼノン(Zeno)積公式:これついて,海外共同研究者P.Exnerとの共同研究で,中間的結果をAnn, H.Poincare(2005)誌に発表した。","subitem_description_type":"Abstract"},{"subitem_description":"In two papers in Commun.Math.Phys. 2001, Ichinose, with Hideo Tamura, Hiroshi Tamura and V.A.Zagrebnov, proved norm convergence of Trotter product formula for the operator sum of two nonnegative selfadjoint operators with optimal error bound. The present research has been done to go beyond this result, keeping in mind its relation to path integral and examples/applications of the theory of Schrodinger operators, and brought the following results.\n(1)Further development of Trotter product formula in norm-It is known that the norm convergence of Trotter product formula does not hold in general for the form sum of two selfadjoint operators. However, it was proved in J. Functional Analysis 2004 with some condition by Ichinose together with H. Neidhardt and V.A. Zagrebnov. It is an open problem whether the condition may be relaxed. To be unexpected,Ichinose and Hideo Tamura also discovered, in Lett. Math. Phys. 2004, norm convergence of the unitary product formula to hold for the Dirac and the relativistic SchrOdinger operator with nontrivial scalar potentials.\n(2)Problems of path integral and of convergence of integral kernels of the Trotter product: Fujiwara succeeded to improve the error estimate of the stationary phase method of the oscillatory integral in large dimensions, and used it to determine the second term of the semiclassical approximation to Feynman path integral. In this connection, Trotter product formula is thought to give a kind of time-sliced approximation. The good norm-convergence of Trotter product formula might suggest convergence of the integral kernels, as Ichinose and Hideo Tamura anticipated. In fact, we proved it 2004 in two papers in Commn. PDE and J. Reine Angew. Math.\n(3)Zeno product formula: Ichinose proved 2005 an intermediate result with P.Exner.","subitem_description_type":"Abstract"}]},"item_9_description_22":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"研究課題/領域番号:16340038, 研究期間(年度):2004 – 2006","subitem_description_type":"Other"},{"subitem_description":"出典：「Trotter積公式の更なる展開と経路積分の問題」研究成果報告書　課題番号16340038\n（KAKEN：科学研究費助成事業データベース（国立情報学研究所））\n（https://kaken.nii.ac.jp/ja/report/KAKENHI-PROJECT-16340038/163400382006kenkyu_seika_hokoku_gaiyo/)を加工して作成","subitem_description_type":"Other"}]},"item_9_description_5":{"attribute_name":"提供者所属","attribute_value_mlt":[{"subitem_description":"金沢大学大学院自然科学研究科","subitem_description_type":"Other"}]},"item_9_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.24517/00063269","subitem_identifier_reg_type":"JaLC"}]},"item_9_relation_28":{"attribute_name":"関連URI","attribute_value_mlt":[{"subitem_relation_name":[{"subitem_relation_name_text":"https://nrid.nii.ac.jp/ja/search/?kw=20024044"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://nrid.nii.ac.jp/ja/search/?kw=20024044","subitem_relation_type_select":"URI"}},{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/ja/grant/KAKENHI-PROJECT-16340038/"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/ja/grant/KAKENHI-PROJECT-16340038/","subitem_relation_type_select":"URI"}},{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/ja/report/KAKENHI-PROJECT-16340038/163400382006kenkyu_seika_hokoku_gaiyo/"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/ja/report/KAKENHI-PROJECT-16340038/163400382006kenkyu_seika_hokoku_gaiyo/","subitem_relation_type_select":"URI"}}]},"item_9_version_type_25":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_ab4af688f83e57aa","subitem_version_type":"AM"}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2021-10-29"}],"displaytype":"detail","filename":"SC-PR-ICHINOSE-T-kaken 2008-2p.pdf","filesize":[{"value":"65.2 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"SC-PR-ICHINOSE-T-kaken 2008-2p.pdf","url":"https://kanazawa-u.repo.nii.ac.jp/record/56995/files/SC-PR-ICHINOSE-T-kaken 2008-2p.pdf"},"version_id":"5a239056-2a8b-47aa-a5b4-09464c51e3d6"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"research report","resourceuri":"http://purl.org/coar/resource_type/c_18ws"}]},"item_title":"Trotter積公式の更なる展開と経路積分の問題","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Trotter積公式の更なる展開と経路積分の問題"},{"subitem_title":"Further Development of Trotter Product Formulas with Problems on Path Integrals","subitem_title_language":"en"}]},"item_type_id":"9","owner":"18","path":["2827"],"pubdate":{"attribute_name":"公開日","attribute_value":"2021-10-29"},"publish_date":"2021-10-29","publish_status":"0","recid":"56995","relation_version_is_last":true,"title":["Trotter積公式の更なる展開と経路積分の問題"],"weko_creator_id":"18","weko_shared_id":-1},"updated":"2023-07-27T14:32:59.199064+00:00"}