Chern-Simons Type Characteristic Classes of Abelian Lattice Gauge Theory

TL;DR

This paper extends Chern-Simons characteristic classes to abelian lattice gauge theory and establishes their differential and coboundary relations using noncommutative calculus.

Contribution

It introduces a lattice version of Chern-Simons classes and links their differential properties to coboundaries in a noncommutative setting.

Findings

Chern-Simons classes are extended to lattice gauge theory.

Differential of a Chern-Simons class equals the coboundary of the previous class.

Establishes a noncommutative calculus framework for these classes.

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 a 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 classes based upon the noncommutative differential calculus on the lattice.