Difference Discrete Connection and Curvature on Cubic Lattice

Details Difference Discrete Connection and Curvature on Cubic Lattice Difference Discrete Connection and Curvature on Cubic Lattice

2007-07-25

arxiv.org/abs/0707.3741v1

Science in China Series A: Mathematics 49(2006)1458

Physics

Mathematical Physics

29 pages

Scientific paper

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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