  In this work, we present a brief but insightful overview of the gauge
theories, which are defined on $ n $-dimensional lattices by using finite gauge
groups, in order to show how they can be interpreted as a Hamiltonian system
with constraints, analogous to what happens with the classical (continuous)
gauge (field) theories. As this interpretation is not usually explored in the
literature that discusses/introduces the concept of lattice gauge theory, but
some recent works have been exploring Hamiltonian models in order to support
some kind of quantum computation, we use this interpretation to, for example,
present a brief geometric view of one class of these models: the Kitaev Quantum
Double Models.
