Difference discrete connection and curvature on cubic lattice |
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Authors: | WU Ke ZHAO Weizhong GUO Hanying |
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Affiliation: | 1. Department of Mathematics, Capital Normal University, Beijing 100037, China 2. 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. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday |
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Keywords: | discrete connection discrete curvature noncommutative calculus lattice gauge theory discrete Lax pair |
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