Construction of Fuzzy Spaces and Their Applications to Matrix Models
スポンサーリンク
概要
- 論文の詳細を見る
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.
- 素粒子論グループ 素粒子研究編集部の論文
- 2006-07-20
著者
関連論文
- Construction of Fuzzy Spaces and Their Applications to Matrix Models
- Fuzzy S^4 and Its Construction(Field theory, Lattice and Noncommutative space,NONCOMMUTATIVE GEOMETRY AND QUANTUM SPACETIME IN PHYSICS)