2000 Fiscal Year Final Research Report Summary
The construction of the field theory on the noncommutative spaces and its application
| Project/Area Number |
09640331
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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 |
素粒子・核・宇宙線
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| Research Institution | TOHOKU UNIVERSITY |
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Principal Investigator |
WATAMURA Satoshi Tohoku University, Graduate School of Science, associate professor, 大学院・理学研究科, 助教授 (00201252)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIKAWA Hiroshi Tohoku University, Graduate School of Science, assistant, 大学院・理学研究科, 助手 (20291247)
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| Project Period (FY) |
1997 – 2000
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| Keywords | Noncommutative geometry / Quantum space / Field theory / Matrix theory / Noncommutative sphere / D-brane |
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| Research Abstract |
The aim of this research is to construct the field theory over the non-commutative space and to analyze its physical properties. In the last 4 years research supported by the present Grant-in-Aid we have been especially investigating the field theory on the non-commutative sphere as a concrete example of a non-commutative curved space. The non-commutative sphere is defined by quantizing the algebra over the 2-sphere. As a first step in this direction we have constructed the non-commutative differential algebra according to the approach given by Connes (paper 1), and as its application we formulated the scalar field on the non-commutative sphere (paper 2). Our main interest is to define the gauge theory on the non-commutative sphere. However, for this end we had to analyze further detailed structure of the differential calculus. In paper 3 we succeeded to formulated the U (1) gauge theory, and we have analyzed its commutative limit. Especially in gauge theory we obtained a new term and the structure of this new term, which does not have a correspondence in the commutative case, gives us a tool to classify the gauge theory on the non-commutative sphere.
Recently, it is found that the D-brane which wraps around the torus possesses a non-commutative structure in the background of an antisymmetric tensor field. It is an interesting problem to investigate the ralation between string theory and non-commutative geometry. From this point of view we investigated the D-brane in the group manifold and constructed the boundary state in the SU (2) manifold (paper 5). The effective theory of this D-brane in SU (2) is given by the gauge thoery on the non-commutative sphere described above and we are presently researching those relations.
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Research Products
(12 results)
