Abstract In this paper, we consider an extended Kazakov–Migdal model defined on arbitrary graph. The partition function of the model, which is expressed as summation all Wilson loops graph, turns out to be represented by Bartholdi zeta weighted unitary matrices edges cycle graph at finite N generating generalized Catalan numbers. can exactly evaluated large N, infinite product a kind deformed I...

Based upon the mathematical formulas of Lattice gauge theory and non-commutative geometry differential calculus, we developed an approach of generalized gauge theory on a product of the spacetime lattice and the two discrete points(or a Z2 discrete group). We introduce a differentiation for non-nearest-neighbour points and find that this differentiation may lead to the introduction of Wilson te...