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Noncommutative Differential Calculus and Its Application on the Lattice 被引量：2

格点上的非交换微分运算及其应用(英文)
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摘要 By introducing the noncommutative differential calculus on the function space of the infinite/finite set and construct a homotopy operator, one prove the analogue of the Poincare lemma for the difference complex. As an application of the differential calculus, a two dimensional integral model can be derived from the noncommutative differential calculus.
作者 刘震 白永强 李起升
机构地区 Center of Mathematical Sciences Department of Mathematics College of Mathematics and Information Science Institute of Mathematics
出处 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第2期245-251,共7页 数学季刊（英文版）
基金 Supported by the China Pcetdoctoral Science Foundation by a grant from Henan University(05YBZR014) Supported by the Tianyuan Foundation for Mathematics of National Natural Science Foundation of China(10626016)
关键词 noncommutative geometry noncommutative differential calculus Poincare lemma Toda lattice equation 格点 非交换微分运算 非交换几何学 格子方程
分类号 O186.15 [理学—基础数学]
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参考文献9

  • 1CONNES A.Noncommutative Geometry[M].INC:Academic Press,1994.
  • 2CONNES A,LOTT J.Particle models and noncommutative geometry[J].Nucl Phys B Proc Suppl,1990,18B:29-47.
  • 3CHAMSEDDINE A H,Connes A.Universal formula for noncommutative geometry actions:unification of gravity and the standard model[J].Phys Rev Lett,1996,77(24):4868-4871.
  • 4CONNES A.DOUGLAS M,SCHWARTZ A.Noncommutative geometry and matrix theory:compactifica-tion on tori[J].J High Energy Phys,1998,02:003-037.
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  • 7GUO H Y,WU K,ZHANG W.Noncommutative differential calculus on Abelian groups and its applications[J].Comm Theo Phys,2000,34:245-250.
  • 8GUO H Y,WU K.On variations in discrete mechanics and field theory[J].J Math Phys,2003,44:5978-6004.
  • 9HYDON P E,MANSFIELD E L.A variational complex for difference equations[J].Found Comp Math,2004,4:187-217.

同被引文献26

  • 1OLVER P J. Applications of Lie Groups to Differential Equations[M]. New York: Springer-Verlag, 1993.
  • 2CONNES A. Noncommutative Geometry[M]. Academic Press, 1994.
  • 3CONNES A, LOTT J. Particle models and noncommutative geometry[J]. Nucl Phys B Proc Suppl, 1990, 18B: 29-47.
  • 4CHAMSEDDINE A H, CONNES A. Universal formula for noncommutative geometry actions: unification of gravity and the standard model[J]. Phys Rev Lett, 1996, 77(24): 4868-4871.
  • 5CONNES A, DOUGLAS M, SCHWARTZ A. Noncommutative geometry and matrix theory: compactification on tori[J]. J High Energy Phys, 1998, 02: 003-037.
  • 6GUO Han-ying, WU Ke. On variations in discrete mechamics and field theory[J]. J Math Phys, 2003, 44: 5978-6004.
  • 7GUO Han-ying, WU Ke. Noncommutative differential calculus on Abelian groups and its applications[J]. Comm Theo Phys, 2000, 34: 245-250.
  • 8HYDON P E, MANSFIELD E L. A variational complex for difference equations[J]. Foundations of Computional Mathematica, 2004, 4: 187-217.
  • 9MARATHE K B, MARTUCCI G. The Mathematical Foundation of Gauge Theories[M]. North-Holland Elsevier Science Publishers, 1902.
  • 10SCHOEN R, YAU S T. Positivity of the total mass of a general space-time[J]. Phys Rev Lett, 1979, 43 1457-1459.

引证文献2

Chinese Quarterly Journal of Mathematics
2007年 第2期

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