| 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 (2001) Dept.Math.,Tokyo University of Science Prof., 理工学部, 教授 (20087018)
荒木 不二洋 (1999-2000) 東京理科大学, 理工学部, 教授 (20027361)
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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)
大森 英樹 東京理科大学, 理工学部, 教授 (20087018)
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| Project Period (FY) |
2000 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2001: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2000: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1999: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | CFT / Deformation quantization / 部分因子環 / 既約指標 / 作用素凸関係 / XY鎖 / 二次元共形場 / ワイル順序付け表式 / *積 / モワイヤル積 / 数理物理学 |
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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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