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Difference discrete connection and curvature on cubic lattice

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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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Authors and Affiliations

  1. Department of Mathematics, Capital Normal University, Beijing, 100037, China

    Wu Ke & Zhao Weizhong

  2. Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100080, China

    Guo Hanying

Authors
  1. Wu Ke
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  2. Zhao Weizhong
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  3. Guo Hanying
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Corresponding author

Correspondence to Wu Ke.

Additional information

Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

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Wu, K., Zhao, W. & Guo, H. Difference discrete connection and curvature on cubic lattice. SCI CHINA SER A 49, 1458–1476 (2006). https://doi.org/10.1007/s11425-006-2060-y

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  • DOI: https://doi.org/10.1007/s11425-006-2060-y

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