Chern-Simons type characteristic classes of Abelian lattice gauge theory

Abstract

In this paper, we extend the definition of the Chern-Simons type characteristic classes in the continuous case to Abelian lattice gauge theory. Then, we show that the exterior differential of the k-th Chern-Simons type characteristic class is exactly equal to the coboundary of the cochain of the $(k-1)$-th Chern-Simons type characteristic class based upon the noncommutative differential calculus on the lattice.