{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T02:28:03Z","timestamp":1649125683212},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2007,9]]},"abstract":"<jats:p>On the basis of the mathematical notion of \u201cmicro-macro duality\u201d for understanding mutual relations between microsopic quantum systems (micro) and their macroscopic manifestations (macro) in terms of the notion of sectors and order parameters, a general mathematical scheme is proposed for detecting the state-structure inside of a sector through measurement processes of a maximal abelian subalgebra of the algebra of observables. For this purpose, the Kac-Takesaki operators controlling group duality play essential roles, which naturally leads to the composite system of the observed system and the measuring system formulated by a crossed product. This construction of composite systems will be shown to make it possible for the micro to be reconstructed from its observational data as macro in the light of the Takesaki duality for crossed products.<\/jats:p>","DOI":"10.1007\/s11080-007-9054-2","type":"journal-article","created":{"date-parts":[[2007,9,14]],"date-time":"2007-09-14T06:38:26Z","timestamp":1189751906000},"page":"307-318","source":"Crossref","is-referenced-by-count":3,"title":["How to Observe Quantum Fields and Recover Them From Observational Data?"],"prefix":"10.1142","volume":"14","author":[{"given":"Izumi","family":"Ojima","sequence":"first","affiliation":[{"name":"Research Institute for Mathematical Sciences, Kyoto University Kyoto 606\u20138502, Japan"}]},{"given":"Mitsuharu","family":"Takeori","sequence":"additional","affiliation":[{"name":"Research Institute for Mathematical Sciences, Kyoto University Kyoto 606\u20138502, Japan"}]}],"member":"219","published-online":{"date-parts":[[2012,4,17]]},"reference":[{"key":"rf4","volume-title":"Von Neumann Algebras","author":"Dixmier J.","year":"1981"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6188-9"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.2307\/2373525"},{"key":"rf8","volume-title":"Lecture Notes in Mathematics","author":"Nakagami Y.","year":"1979"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02813-1"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2004.12.003"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392041"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-10451-4"},{"key":"rf15","doi-asserted-by":"crossref","first-page":"133","DOI":"10.24033\/asens.1247","volume":"6","author":"Connes A.","journal-title":"Ann. Sci. \u00b4Ecole Norm. Sup. S\u00e9r. 4"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/BF01217805"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1007\/s11080-007-9054-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,26]],"date-time":"2020-04-26T13:53:15Z","timestamp":1587909195000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1007\/s11080-007-9054-2"}},"subtitle":["Takesaki Duality as a Micro-Macro Duality"],"short-title":[],"issued":{"date-parts":[[2007,9]]},"references-count":10,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,4,17]]},"published-print":{"date-parts":[[2007,9]]}},"alternative-id":["10.1007\/s11080-007-9054-2"],"URL":"https:\/\/doi.org\/10.1007\/s11080-007-9054-2","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,9]]}}}