2010 Fiscal Year Final Research Report
Noncommutative deformation of topological invariants in gauge theories
| Project/Area Number |
20740049
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Kushiro National College of Technology |
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Principal Investigator |
SAKO Akifumi Kushiro National College of Technology, 一般教科, 准教授 (00424200)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 非可換幾何 / ゲージ理論 |
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| Research Abstract |
Solitons in gauge theories in noncommutative spaces had been constructed by using several methods. However we did not have noncommutative soliton solutions by using deformation quantization from solitons in commutative soliton solutions, and we did not have researches for such solutions. In this study, we do them for the case of instantons that are solitons in a 4-dimensional gauge theory. Deformation quantization of instanton solutions for U(N) (N>1) gauge theory in R4 is constructed and it is shown that their instanton numbers are preserved under the deformation quantization. We also derive the one-to-one correspondence between the instantons and ADHM data.
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