2006 Fiscal Year Final Research Report Summary
The study of the axiomatic quantum field theory using ultrahyperfunctions
| Project/Area Number |
16540159
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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, Institute of Technology and Science, Professor, ソシオテクノサイエンス研究部, 教授 (00030784)
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| Project Period (FY) |
2004 – 2006
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| Keywords | Fundamental length / Ultrahyperfunction |
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| Research Abstract |
It is shown in the paper of E. Bruening and S. Nagamachi "Relativistic quantum field theory with a fundamental length" published in Journal of Mathematical Physics in 2004 that if we use the theory of ultrahyperfunctions we can formulate a quantum field theory with a fundamental length. Here the fundamental length 1 has the property that the two events occurring within the length 1 cannot be distinguished. Such a theory cannot be formulated by using distributions or hyperfunctions.
The theory with a fundamental length has a history since 1930's. The speed c of light is a fundamental constant in relativity theory and Planck's constant h is the fundamental constant of quantum mechanics. Since the quantum field theory is the combination of relativity and quantum mechanics, the Dirac field equation has both constants c and h. The dimension of c is [L/T] and that of h is [MLL/T]. W. Heisenberg thought that a fundamental equation of Physics must also contain a constant 1 with the dimension of
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length [L]. If such a constant 1 is introduced, then the dimensions of any other quantity can be expressed in terms of combinations of the basic constants c, h, and 1. In 1958, Heisenberg and Pauli introduced an equation which was later called the equation of the universe. This equation has a constant 1 with the dimension [L] but unfortunately, nobody has been able to solve this equation.
We consider the linearized version of this equation which inherits the important constant 1 with the dimension [L]. The paper "HEISENBERG'S FUNDAMENTAL EQUATION AND QUANTUM FIELD THEORY WITH A FUNDAMENTAL LENGTH" written by Prof. E. Bruening and S. Nagamachi shows that one cannot solve this model within the standard framework using distributions or hyperfunctions but can solve within the framework of our previous paper: Relativistic quantum field theory with a fundamental length. Moreover, the constant 1 with the dimension [L] of the model is shown to be the fundamental length introduced in this paper. Less
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Research Products
(2 results)
