Dynamics of fields and particles in a 5-dimensional scenario : problems and perspectives of the Kaluza-Klein theory

In this work a revised study of the compactified 5D Kaluza-Klein ( KK ) model is performed. At first, it is proved the compatibility of ADM slicing with respect to the KK reduction and the Hamiltonian formulation of the model is therefore obtained: this analysis envisages how the Gauss constraint arises as a particular case of supermomenta constraints; moreover, it is shown that the hamiltonian constraint can be solved with respect to the conjugate momentum of the metric scalar field, thus allowing to write a Schroedinger-like equation via a Brown-Kuchar approach. Thereafter the problem of matter coupling is addressed and a new approach is proposed; in such a scheme a 5D cylindrical energy-momentum tensor is postulated and the dynamics of test particle is faced via a proper localization hypothesis by mean of a multipole expansion a lá Papapetrou. The particles turns out to be delocalized into the extra dimension and the tower of huge massive modes is removed. Such a result allows us to deal consistently with matter without discarding the compactification hypothesis. Therefore a full model, involving metric fields and matter is formulated, where an extra scalar source term appears and the rest mass of particles is varying depending on scalar fields (the metric one plus the source one). Promising scenarios, in order to deal with unification scheme and dark matter models are outlined.