2013 Fiscal Year Final Research Report
Spectral analysis of quantum field theory on curved space time and its application
| Project/Area Number |
24740084
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Shinshu University |
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Principal Investigator |
SUZUKI Akito 信州大学, 工学部, 助教 (70585611)
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| Project Period (FY) |
2012-04-01 – 2014-03-31
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| Keywords | 場の量子論 / スペクトル / グラフ |
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| Research Abstract |
The spectral properties of particle systems on curved spacetime were analyzed. Particularly, descretized spaces are viewed as graphs, and the relation between the spectra of many-particle systems and the structure of graphs where the particles move was studied. The zero eigenspace and the Witten index of the particle Hamiltonians were proved to be invariant under a graph transformation. The spectral gap was shown to remain open under the same graph transfomation as above.
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