1999 Fiscal Year Final Research Report Summary
The Study of Hyperfunction Quantum Field Theory
| Project/Area Number |
10640174
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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 |
Basic analysis
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| Research Institution | The University of Tokushima |
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Principal Investigator |
NAGAMACHI Shigeaki The University of Tokushima, Faculty of Engineering, Professor, 工学部, 教授 (00030784)
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| Co-Investigator(Kenkyū-buntansha) |
OKAMOTO Kuniya The University of Tokushima, Faculty of Engineering, Lecturer, 工学部, 講師 (90263871)
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| Project Period (FY) |
1998 – 1999
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| Keywords | hyperfunction / quantum field / operator algebra |
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| Research Abstract |
The relativity and quantum mechanics, which are big discoveries in physics in the 20-th century, are combined into the quantum field theory, which is relativistic quantum mechanics. The quantum field theory is characterized by its Wightman functions. The Wightman functions are generalized functions and usually we consider the so called the standard quantum field theory, where the Wightman functions are Schwartz's tempered distributions. The hyperfunction is considered to be the most general one among generalized functions that has the local properties. Therefore the quantum fields which correspond to hyperfunctions (more precisely, the quantum field whose Wightman functions are Fourier hyperfunctions) are considered to be the most general and studied since 1976 by the author. Since the test-function space of Fourier hyperfunctions consists of analytic functions, it does not contain functions of compact supports. This fact makes the study of hyperfunction quantum field theory (HFQFT) difficult.
This time, we have the following results: (1) Since there are no functions with compact supports in the test-function space of Fourier hyperfunctions, we cannot define the field operator restricted in the bounded region in the framework of HFQFT. Nevertheless we could prove that we can define the operators and operator algebras which correspond to the observables in the bounded region (1998).
(2) We proved the existence of the model of HFQFT which has the nontrivial operator algebras which correspond to the set of observables in the bounded region.
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Research Products
(4 results)
