  We consider quiver representations not on vector spaces, as traditional, but
on a different target category, which emerges in the context of noncommutative
geometry. The equivalence between quiver representations and path algebra
modules -- established here for the new category -- inspired the following
construction: Only from representation theory data, we build the Dirac operator
(of a spectral triple) on a quiver and evaluate the spectral action functional
from a general formula over closed paths derived here. We apply this
construction to gauge theories on lattice-quivers and obtain all the exact
Weisz-Wohlert-type cells in the context of Symanzik's improvement to the
Wilsonian Yang-Mills lattice gauge theory. We show that a hermitian Higgs field
emerges from the self-loops of the quiver and derive the Yang-Mills--Higgs
theory on flat space as a limit of certain quivers. We worked in arbitrary
dimension and, concerning paths on lattices, we proved some combinatorial
claims, which might be useful elsewhere.
