ON THE ADM DECOMPOSITION OF THE 5-D KALUZA–KLEIN MODEL

Abstract

Our purpose is to recast the KK model in terms of ADM variables. We examine and solve the problem of the consistency of this approach, with particular care about the role of the cylindricity hypothesis. We show in detail how the KK reduction commutes with the ADM slicing procedure and how this leads to a well-defined and unique ADM reformulation. This allows us to consider the Hamiltonian formulation of the model and moreover it can be viewed as the first step for the Ashtekar reformulation of the KK scheme. Moreover, we show how the time component of the gage vector arises naturally from the geometrical constraints of the dynamics; this is a positive check for the autoconsistency of the KK theory and for an Hamiltonian description of the dynamics which will take into account the compactification scenario; this result enforces the physical meaning of the KK model.