Difference discrete connection and curvature on cubic lattice  

作　　者：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 

出　　处：《Science China Mathematics》2006年第11期1458-1476,共19页中国科学：数学（英文版）

基　　金：Acknowledgements This work was partly supported by the National Key Basic Research Program of China(Grant No.2004CB318000);the National Natural Science Foundation of China(Grant No.10375087,10375038,90403018,90503002).

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.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.

关 键 词：DISCRETE connection  DISCRETE curvature  NONCOMMUTATIVE calculus  lattice gauge theory  DISCRETE LAX pair. 

分 类 号：O186.1[理学—数学]