Hamiltonian Formulation of 5-dimensional Kaluza-Klein Theory

We analyze the consistency of the ADM approach to KK model; we prove that KK reduction commute with ADM splitting. This leads to a well defined Hamiltonian; we provide the outcome. The electromagnetic constraint is derived from a geometrical one and this result enforces the physical meaning of KK model. Moreover we study the role of the extra scalar field we have in our model; classical hints from geodesic motion and cosmological solutions suggest that the scalar field can be an alternative time variable in the relational point of view.