F. Cardone, A. Marrani, R. Mignani
We illustrate the main features of a new Kaluza-Klein-like scheme (Deformed Relativity in five dimensions). It is based on a five-dimensional Riemannian space in which the four-dimensional space-time metric is deformed (i.e. it depends on the energy) and energy plays the role of the fifth dimension. We review the solutions of the five-dimensional Einstein equations in vacuum and the geodetic equations in some cases of physical relevance. The Killing symmetries of the theory for the energy-dependent metrics corresponding to the four fundamental interactions (electromagnetic, weak, strong and gravitational) are discussed for the first time. Possible developments of the formalism are also briefly outlined.