Wilson Action of Lattice Gauge Fields with An Additional Term from Noncommutative Geometry

Differential structure of lattices can be defined if the lattices are treated as models of noncommutative geometry. The detailed construction consists of specifying a generalized Dirac operator and a wedge product. Gauge potential and field strength tensor can be defined based on this differential structure. When an inner product is specified for differential forms, classical action can be deduced for lattice gauge fields. Besides the familiar Wilson action being recovered, an additional term, related to the non-unitarity of link variables and loops spanning no area, emerges.