2001 Fiscal Year Final Research Report Summary
2-dineusional couformal field theory and subfactors
| Project/Area Number |
11640214
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
HIDEKI Omori Dept.Math.,Tokyo University of Science Prof., 理工学部, 教授 (20087018)
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| Co-Investigator(Kenkyū-buntansha) |
TOSHIAKI Shoji Dept.Math.,Tokyo University of Science Prof., 理工学部, 教授 (40120191)
NOBUKAZU Otuki Dept.Math.,Tokyo University of Science Prof., 理工学部, 教授 (80112895)
REIDO Kobayashi Dept.Math.,Tokyo University of Science Prof., 理工学部, 教授 (70120186)
KENRO Furutani Dept.Math.,Tokyo University of Science Prof., 理工学部, 教授 (70112901)
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| Project Period (FY) |
2000 – 2001
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| Keywords | CFT / Deformation quantization |
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| Research Abstract |
In this term. it is getting clear that the mathematical research of quantum physic is not a research of physic, but a research of the way of recognition of the quantum world, or the research for finding new concept which express correctly the quantum world.
In this direction, we propose a new mathematical notion, p-regulated algebras which includes the notion of formal deformation quantization and quasntizations where h is not treated as a formal parameter.
In an extension of such algebras where h is not treated as a formal parameter, we lined several anomalous fact such as a single element has two different inverses, or has left inverse a right inverse at the same time. These phenomena show taht the associativity breaks down in such extended object. In order to avoid such anomalous phenomena, one has to break some symmetry by complex multiplication, and one has to restrict. the whole system in the coefficients of real numbers.
Moreover, the "group" generated by the *-exponential functions of quadratic forms be haves as if it were the non-tivial double cover of SL(2 ; C), which is simply connected. Here the notion of "point" is by no means a absolute notion, but only a local notion. This seems to correspond that an individual electron has a meaning in only a very restricted situation.
To make such "anomalous phenomena" an "ordinary phenomena" in the quantum world one has to invent some new way of recognition, which must be a very now experiance of mathematics
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Research Products
(7 results)
