2013 Fiscal Year Final Research Report
On the theory of the oscillatory integral operators and its applications to the Feyman path integral for the field theory
| Project/Area Number |
23540195
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Shinshu University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
SASAKI Itaru 信州大学, 理学部, 助教 (50558161)
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| Project Period (FY) |
2011 – 2013
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| Keywords | Feyman 経路積分 / Dirac 方程式 / 量子電磁気学 / 量子力学 / Schroedinger 方程式 |
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| Research Abstract |
The applicant succeeded in giving the expression of the Feynman path integral for the solutions of the Dirac equations, which describe the quantum particles in the relativistic theory. In more general, the expression of the Feynman path integral was given for the solutions of more general equations including the Dirac ones.
This expression is given in the form of the "sum" of the probability amplitude satisfying the superposition principle over all possible paths that go in any direction at any speed forward and backward in time. The electrons that go backward in time are interpreted as positrons that go forward in time. This expression enables us to understand the relativistic quantum mechanics intuitively and to expect that we can construct the relativistic quantum electrodynamics in terms of a more direct method than the perturbative one used mainly in the present. The Feynman path integral for the Dirac equations has not been given for 60 years or more.
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