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Difference discrete connection and curvature on cubic lattice Dedicated to Professor Sheng GONG on the occasion of his 75th birthday
引用本文:WU Ke,ZHAO Weizhong & GUO Hanying Department of Mathematics,Capital Normal University,Beijing 100037,China, Institute of Theoretical Physics,Chinese Academy of Sciences,Beijing 100080,China. Difference discrete connection and curvature on cubic lattice Dedicated to Professor Sheng GONG on the occasion of his 75th birthday[J]. 中国科学A辑(英文版), 2006, 0(11)
作者姓名:WU Ke  ZHAO Weizhong & GUO Hanying Department of Mathematics  Capital Normal University  Beijing 100037  China   Institute of Theoretical Physics  Chinese Academy of Sciences  Beijing 100080  China
作者单位:WU Ke,ZHAO Weizhong & GUO Hanying Department of Mathematics,Capital Normal University,Beijing 100037,China; Institute of Theoretical Physics,Chinese Academy of Sciences,Beijing 100080,China
摘    要:In a way similar to the continuous case formally, we define in different but equivalent manners the difference discrete connection and curvature on discrete vector bundle over the regular lattice as base space. We deal with the difference operators as the discrete counterparts of the derivatives based upon the differential calculus on the lattice. One of the definitions can be extended to the case over the random lattice. We also discuss the relation between our approach and the lattice gauge theory and apply to the discrete integrable systems.


Difference discrete connection and curvature on cubic lattice Dedicated to Professor Sheng GONG on the occasion of his 75th birthday
WU Ke,ZHAO Weizhong , GUO Hanying. Difference discrete connection and curvature on cubic lattice Dedicated to Professor Sheng GONG on the occasion of his 75th birthday[J]. Science in China(Mathematics), 2006, 0(11)
Authors:WU Ke  ZHAO Weizhong & GUO Hanying
Affiliation:WU Ke,ZHAO Weizhong & GUO Hanying Department of Mathematics,Capital Normal University,Beijing 100037,China, Institute of Theoretical Physics,Chinese Academy of Sciences,Beijing 100080,China
Abstract:In a way similar to the continuous case formally, we define in different but equivalent manners the difference discrete connection and curvature on discrete vector bundle over the regular lattice as base space. We deal with the difference operators as the discrete counterparts of the derivatives based upon the differential calculus on the lattice. One of the definitions can be extended to the case over the random lattice. We also discuss the relation between our approach and the lattice gauge theory and apply to the discrete integrable systems.
Keywords:discrete connection   discrete curvature   noncommutative calculus   lattice gauge theory   discrete Lax pair.
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