Soryushiron Kenkyu Electronics
Online ISSN : 2433-2895
Print ISSN : 0371-1838
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Volume 113, Issue 4
Displaying 1-11 of 11 articles from this issue
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  • [title in Japanese]
    Article type: Cover
    2006 Volume 113 Issue 4 Pages Cover1-
    Published: July 20, 2006
    Released on J-STAGE: October 02, 2017
    DOIhttps://doi.org/10.24532/soken.113.4_Cover1
    JOURNAL FREE ACCESS
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  • [title in Japanese]
    Article type: Appendix
    2006 Volume 113 Issue 4 Pages App1-
    Published: July 20, 2006
    Released on J-STAGE: October 02, 2017
    DOIhttps://doi.org/10.24532/soken.113.4_App1
    JOURNAL FREE ACCESS
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  • [title in Japanese]
    Article type: Appendix
    2006 Volume 113 Issue 4 Pages D1-D2
    Published: July 20, 2006
    Released on J-STAGE: October 02, 2017
    DOIhttps://doi.org/10.24532/soken.113.4_D1
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  • Construction of Fuzzy Spaces and Their Applications to Matrix Models
    Yasuhiro Abe
    Article type: Article
    2006 Volume 113 Issue 4 Pages 7-75
    Published: July 20, 2006
    Released on J-STAGE: October 02, 2017
    DOIhttps://doi.org/10.24532/soken.113.4_7
    JOURNAL FREE ACCESS
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    Quantization of spacetime by means of finite dimensional matrices is the basic idea of fuzzy spaces. There remains an issue of quantizing time, however, the idea is simple and it provides an interesting interplay of various ideas in mathematics and physics. Shedding some light on such an interplay is the main theme of this dissertation. The dissertation roughly separates into two parts. In the first part, we consider rather mathematical aspects of fuzzy spaces, namely, their construction. We begin with a review of construction of fuzzy complex projective spaces CP^κ (κ=1, 2,・・・) in relation to geometric quantization. This construction facilitates defining symbols and star products on fuzzy CP^κ. Algebraic construction of fuzzy CP^κ is also discussed. We then present construction of fuzzy S^4, utilizing the fact that CP^3 is an S^2 bundle over S^4. Fuzzy S^4 is obtained by imposing an additional algebraic constraint on fuzzy CP^3. Consequently it is proposed that coordinates on fuzzy S^4 are described by certain block-diagonal matrices. It is also found that fuzzy S^8 can analogously be constructed. In the second part of this dissertation, we consider applications of fuzzy spaces to physics. We first consider theories of gravity on fuzzy spaces, anticipating that they may offer a novel way of regularizing spacetime dynamics. We obtain actions for gravity on fuzzy S^2 and on fuzzy CP^2 in terms of finite dimensional matrices. Application to M(atrix) theory is also discussed. With an introduction of extra potentials to the theory, we show that it also has new brane solutions whose transverse directions are described by fuzzy S^4 and fuzzy CP^3. The extra potentials can be considered as fuzzy versions of differential forms or fluxes, which enable us to discuss compactification models of M(atrix) theory. In particular, compactification down to fuzzy S^4 is discussed and a realistic matrix model of M-theory in four-dimensions is proposed.
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  • [title in Japanese]
    [in Japanese]
    Article type: Article
    2006 Volume 113 Issue 4 Pages 76-83
    Published: July 20, 2006
    Released on J-STAGE: October 02, 2017
    DOIhttps://doi.org/10.24532/soken.113.4_76
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  • [title in Japanese]
    Article type: Appendix
    2006 Volume 113 Issue 4 Pages App2-
    Published: July 20, 2006
    Released on J-STAGE: October 02, 2017
    DOIhttps://doi.org/10.24532/soken.113.4_App2
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    Download PDF (15K)
  • [title in Japanese]
    Article type: Appendix
    2006 Volume 113 Issue 4 Pages App3-
    Published: July 20, 2006
    Released on J-STAGE: October 02, 2017
    DOIhttps://doi.org/10.24532/soken.113.4_App3
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  • [title in Japanese]
    Article type: Appendix
    2006 Volume 113 Issue 4 Pages App4-
    Published: July 20, 2006
    Released on J-STAGE: October 02, 2017
    DOIhttps://doi.org/10.24532/soken.113.4_App4
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  • [title in Japanese]
    Article type: Appendix
    2006 Volume 113 Issue 4 Pages App5-
    Published: July 20, 2006
    Released on J-STAGE: October 02, 2017
    DOIhttps://doi.org/10.24532/soken.113.4_App5
    JOURNAL FREE ACCESS
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  • [title in Japanese]
    Article type: Cover
    2006 Volume 113 Issue 4 Pages Cover2-
    Published: July 20, 2006
    Released on J-STAGE: October 02, 2017
    DOIhttps://doi.org/10.24532/soken.113.4_Cover2
    JOURNAL FREE ACCESS
    Download PDF (12K)
  • [title in Japanese]
    Article type: Cover
    2006 Volume 113 Issue 4 Pages Cover3-
    Published: July 20, 2006
    Released on J-STAGE: October 02, 2017
    DOIhttps://doi.org/10.24532/soken.113.4_Cover3
    JOURNAL FREE ACCESS
    Download PDF (12K)
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