Fuzzy S^4 and Its Construction(Field theory, Lattice and Noncommutative space,NONCOMMUTATIVE GEOMETRY AND QUANTUM SPACETIME IN PHYSICS)

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概要

• 論文の詳細を見る

• We 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. Hence, as in the case of fuzzy CP^3=SU(4)/U(3), fuzzy S^4 is globally defined on R^<dimSU(4)> with the additional constraint on top of the construction of fuzzy CP^3. We consider the commutative limit of fuzzy S^4 and find that it naturally gives commutative S^4 in terms of homogeneous coordinates on CP^3. We also discuss exact matrix-function correspondence of fuzzy S^4. In conclusion, it is proposed that fuzzy S^4 is described by a certain form of block-diagonal matrix whose embedding square matrix represents fuzzy CP^3.

• 理論物理学刊行会の論文
• 2008-03-07

著者

• Abe Yasuhiro

  Physics Department, City College of the CUNY

• Abe Yasuhiro

  Physics Department City College Of The Cuny

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)

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