{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T22:51:59Z","timestamp":1690930319280},"reference-count":37,"publisher":"AIP Publishing","issue":"11","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2001,11,1]]},"abstract":"<jats:p>Classical Calogero\u2013Moser models with rational potential are known to be superintegrable. That is, on top of the r involutive conserved quantities necessary for the integrability of a system with r degrees of freedom, they possess an additional set of r\u22121 algebraically and functionally independent globally defined conserved quantities. At the quantum level, Kuznetsov uncovered the existence of a quadratic algebra structure as an underlying key for superintegrability for the models based on A type root systems. Here we demonstrate in a universal way the quadratic algebra structure for quantum rational Calogero\u2013Moser models based on any root systems.<\/jats:p>","DOI":"10.1063\/1.1404387","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T12:45:28Z","timestamp":1027687528000},"page":"5329-5340","update-policy":"http:\/\/dx.doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":12,"title":["Quadratic algebra associated with rational Calogero-Moser models"],"prefix":"10.1063","volume":"42","author":[{"given":"R.","family":"Caseiro","sequence":"first","affiliation":[{"name":"Universidade de Coimbra, Departamento de Matem\u00e1tica, 3000\u2009Coimbra, Portugal"}]},{"given":"J.-P.","family":"Fran\u00e7oise","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Paris 6, Laboratoire \u201cGSIB,\u201d 125 Rue du Chevaleret, 75013, Paris, France"}]},{"given":"R.","family":"Sasaki","sequence":"additional","affiliation":[{"name":"Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto\u2009606-8502, Japan"}]}],"member":"317","reference":[{"key":"2023062800435875400_r1","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1063\/1.1665604","volume":"12","year":"1971","journal-title":"J. Math. Phys."},{"key":"2023062800435875400_r2","doi-asserted-by":"crossref","first-page":"1372","DOI":"10.1103\/PhysRevA.5.1372","volume":"5","year":"1972","journal-title":"Phys. Rev. A"},{"key":"2023062800435875400_r3","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/0001-8708(75)90151-6","volume":"16","year":"1975","journal-title":"Adv. Math."},{"key":"2023062800435875400_r3a"},{"key":"2023062800435875400_r3b","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1007\/BF02742674","volume":"13","year":"1975","journal-title":"Lett. Nuovo Cimento Soc. Ital. Fis."},{"key":"2023062800435875400_r3c","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1007\/BF02790495","volume":"13","year":"1975","journal-title":"Lett. Nuovo Cimento Soc. Ital. Fis."},{"key":"2023062800435875400_r4","first-page":"103","volume":"18","year":"1976","journal-title":"Lett. Nuovo Cimento Soc. Ital. Fis."},{"key":"2023062800435875400_r4a","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/0375-9601(83)90018-X","volume":"95","year":"1983","journal-title":"Phys. Lett. A"},{"key":"2023062800435875400_r5","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1016\/0375-9601(96)00421-5","volume":"218","year":"1996","journal-title":"Phys. Lett. A"},{"key":"2023062800435875400_r6","doi-asserted-by":"crossref","first-page":"3035","DOI":"10.1143\/JPSJ.62.3035","volume":"62","year":"1993","journal-title":"J. Phys. Soc. Jpn."},{"key":"2023062800435875400_r7"},{"key":"2023062800435875400_r8","doi-asserted-by":"crossref","first-page":"4679","DOI":"10.1063\/1.533370","volume":"41","year":"2000","journal-title":"J. Math. Phys."},{"key":"2023062800435875400_r9","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1007\/BF01036128","volume":"65","year":"1985","journal-title":"Theor. Math. Phys."},{"key":"2023062800435875400_r10","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/0370-2693(91)91566-E","volume":"262","year":"1991","journal-title":"Phys. Lett. B"},{"key":"2023062800435875400_r11","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/BF01418964","volume":"37","year":"1976","journal-title":"Invent. Math."},{"key":"2023062800435875400_r11a","first-page":"314","volume":"C71","year":"1981","journal-title":"Phys. Rep."},{"key":"2023062800435875400_r12","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1143\/PTP.102.499","volume":"102","year":"1999","journal-title":"Prog. Theor. Phys."},{"key":"2023062800435875400_r13","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1016\/S0550-3213(98)00568-9","volume":"530","year":"1998","journal-title":"Nucl. Phys. B"},{"key":"2023062800435875400_r14","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1143\/PTP.100.1107","volume":"100","year":"1998","journal-title":"Prog. Theor. Phys."},{"key":"2023062800435875400_r14a","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1143\/PTP.101.487","volume":"101","year":"1999","journal-title":"Prog. Theor. Phys."},{"key":"2023062800435875400_r14b","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1143\/PTP.101.799","volume":"101","year":"1999","journal-title":"Prog. Theor. Phys."},{"key":"2023062800435875400_r14c","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1143\/PTP.102.749","volume":"102","year":"1999","journal-title":"Prog. Theor. Phys."},{"key":"2023062800435875400_r15","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1143\/PTP.103.463","volume":"103","year":"2000","journal-title":"Prog. Theor. Phys."},{"key":"2023062800435875400_r16","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/S0375-9601(98)00903-7","volume":"237","year":"1998","journal-title":"Phys. Lett. A"},{"key":"2023062800435875400_r17","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1090\/S0002-9947-1989-0951883-8","volume":"311","year":"1989","journal-title":"Trans. Am. Math. Soc."},{"key":"2023062800435875400_r18"},{"key":"2023062800435875400_r19","doi-asserted-by":"crossref","first-page":"9033","DOI":"10.1088\/0305-4470\/33\/49\/303","volume":"33","year":"2000","journal-title":"J. Phys. A"},{"key":"2023062800435875400_r20","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/S0375-9601(00)00842-2","volume":"279","year":"2001","journal-title":"Phys. Lett. A"},{"key":"2023062800435875400_r21","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1063\/1.532770","volume":"40","year":"1999","journal-title":"J. Math. Phys."},{"key":"2023062800435875400_r22","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/BF01030108","volume":"6","year":"1971","journal-title":"Theor. Math. Phys."},{"key":"2023062800435875400_r23","doi-asserted-by":"crossref","first-page":"1172","DOI":"10.1063\/1.522651","volume":"16","year":"1975","journal-title":"J. Math. Phys."},{"key":"2023062800435875400_r24","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/0370-2693(92)90166-2","volume":"286","year":"1992","journal-title":"Phys. Lett. B"},{"key":"2023062800435875400_r24a","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1016\/0550-3213(93)90315-G","volume":"401","year":"1993","journal-title":"Nucl. Phys. B"},{"key":"2023062800435875400_r24b","doi-asserted-by":"crossref","first-page":"1285","DOI":"10.1063\/1.532380","volume":"39","year":"1998","journal-title":"J. Math. Phys."},{"key":"2023062800435875400_r25","first-page":"369","volume":"49","year":"1989","journal-title":"Ann. I.H.P. Phys. Theor."},{"key":"2023062800435875400_r26","doi-asserted-by":"crossref","first-page":"4465","DOI":"10.1088\/0305-4470\/31\/19\/012","volume":"31","year":"1998","journal-title":"J. Phys. A"},{"key":"2023062800435875400_r27","unstructured":"P. \n            Tempesta\n          , A. Turbiner, and P. Winternitz, \u201cExact solvability of superintegrable systems,\u201d hep-th\/0011209."}],"container-title":["Journal of Mathematical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jmp\/article-pdf\/42\/11\/5329\/11348069\/5329_1_online.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jmp\/article-pdf\/42\/11\/5329\/11348069\/5329_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,28]],"date-time":"2023-06-28T00:44:17Z","timestamp":1687913057000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jmp\/article\/42\/11\/5329\/231188\/Quadratic-algebra-associated-with-rational"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,11,1]]},"references-count":37,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2001,11,1]]}},"URL":"https:\/\/doi.org\/10.1063\/1.1404387","relation":{},"ISSN":["0022-2488","1089-7658"],"issn-type":[{"value":"0022-2488","type":"print"},{"value":"1089-7658","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2001,11]]},"published":{"date-parts":[[2001,11,1]]}}}