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 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.

12 pages

References in corpus (4)

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• Chern-Simons--Antoniadis-Savvidy forms and standard supergravity
• Higher Chern-Simons-Antoniadis-Savvidy forms based on crossed modules
• Straddling-gates problem in multipartite quantum systems