An introduction to the Kaluza-Klein formulation

We give an elementary introduction to the Kaluza-Klein formulation, in which the gravitational and the electromagnetic fields are represented in the geometry of a five-dimensional space. We show that, in the framework of general relativity, the interaction of a point particle, or of a charged spin-zero field, with a gravitational and an electromagnetic field can be obtained through the metric of a five-dimensional space. We also show that the symmetries of the metric of this five-dimensional space lead to constants of motion for the point particles, or to operators that commute with the Klein--Gordon operator. A common misunderstanding related to the unification of gravitation and electromagnetism given by the Kaluza--Klein formulation is discussed.