| Difference discrete connection and curvature on cubic lattice Dedicated to Professor Sheng GONG on the occasion of his 75th birthday |
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| 作者姓名： | WU Ke ZHAO Weizhong & GUO Hanying |
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| 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 |
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| 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.
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Difference discrete connection and curvature on cubic lattice Dedicated to Professor Sheng GONG on the occasion of his 75th birthday |
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| 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(11). |
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| Authors: | WU Ke ZHAO Weizhong & GUO Hanying |
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| Institution: | 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 |
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| 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. |
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| Keywords: | discrete connection discrete curvature noncommutative calculus lattice gauge theory discrete Lax pair |
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