{"title":"关于闭合凸锥上的CCR和CAR流的注释","authors":"Anbu Arjunan","doi":"10.1142/s0219025721500211","DOIUrl":null,"url":null,"abstract":"For a closed convex cone <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:mi>P</mml:mi></mml:math></inline-formula> in <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> which is spanning and pointed, i.e. <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:mi>P</mml:mi> <mml:mo stretchy=\"false\">−</mml:mo> <mml:mi>P</mml:mi> <mml:mo>=</mml:mo> <mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> and <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:mi>P</mml:mi> <mml:mo stretchy=\"false\">∩</mml:mo><mml:mo stretchy=\"false\">−</mml:mo><mml:mi>P</mml:mi> <mml:mo>=</mml:mo> <mml:mo stretchy=\"false\">{</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">}</mml:mo><mml:mo>,</mml:mo></mml:math></inline-formula> we consider a family of <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>-semigroups over <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:mi>P</mml:mi></mml:math></inline-formula> consisting of a certain family of CCR flows and CAR flows over <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:mi>P</mml:mi></mml:math></inline-formula> and classify them up to the cocycle conjugacy.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":"19 3","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Remarks on CCR and CAR flows over closed convex cones\",\"authors\":\"Anbu Arjunan\",\"doi\":\"10.1142/s0219025721500211\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a closed convex cone <inline-formula><mml:math display=\\\"inline\\\" overflow=\\\"scroll\\\"><mml:mi>P</mml:mi></mml:math></inline-formula> in <inline-formula><mml:math display=\\\"inline\\\" overflow=\\\"scroll\\\"><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> which is spanning and pointed, i.e. <inline-formula><mml:math display=\\\"inline\\\" overflow=\\\"scroll\\\"><mml:mi>P</mml:mi> <mml:mo stretchy=\\\"false\\\">−</mml:mo> <mml:mi>P</mml:mi> <mml:mo>=</mml:mo> <mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> and <inline-formula><mml:math display=\\\"inline\\\" overflow=\\\"scroll\\\"><mml:mi>P</mml:mi> <mml:mo stretchy=\\\"false\\\">∩</mml:mo><mml:mo stretchy=\\\"false\\\">−</mml:mo><mml:mi>P</mml:mi> <mml:mo>=</mml:mo> <mml:mo stretchy=\\\"false\\\">{</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\\\"false\\\">}</mml:mo><mml:mo>,</mml:mo></mml:math></inline-formula> we consider a family of <inline-formula><mml:math display=\\\"inline\\\" overflow=\\\"scroll\\\"><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>-semigroups over <inline-formula><mml:math display=\\\"inline\\\" overflow=\\\"scroll\\\"><mml:mi>P</mml:mi></mml:math></inline-formula> consisting of a certain family of CCR flows and CAR flows over <inline-formula><mml:math display=\\\"inline\\\" overflow=\\\"scroll\\\"><mml:mi>P</mml:mi></mml:math></inline-formula> and classify them up to the cocycle conjugacy.\",\"PeriodicalId\":50366,\"journal\":{\"name\":\"Infinite Dimensional Analysis Quantum Probability and Related Topics\",\"volume\":\"19 3\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-01-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Infinite Dimensional Analysis Quantum Probability and Related Topics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219025721500211\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Infinite Dimensional Analysis Quantum Probability and Related Topics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219025721500211","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Remarks on CCR and CAR flows over closed convex cones
For a closed convex cone P in ℝd which is spanning and pointed, i.e. P−P=ℝd and P∩−P={0}, we consider a family of E0-semigroups over P consisting of a certain family of CCR flows and CAR flows over P and classify them up to the cocycle conjugacy.
期刊介绍：
In the past few years the fields of infinite dimensional analysis and quantum probability have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. The number of first-class papers in these fields has grown at the same rate. This is currently the only journal which is devoted to these fields.
It constitutes an essential and central point of reference for the large number of mathematicians, mathematical physicists and other scientists who have been drawn into these areas. Both fields have strong interdisciplinary nature, with deep connection to, for example, classical probability, stochastic analysis, mathematical physics, operator algebras, irreversibility, ergodic theory and dynamical systems, quantum groups, classical and quantum stochastic geometry, quantum chaos, Dirichlet forms, harmonic analysis, quantum measurement, quantum computer, etc. The journal reflects this interdisciplinarity and welcomes high quality papers in all such related fields, particularly those which reveal connections with the main fields of this journal.
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