Five-dimensional quantum mechanics

Summary

In this paper we consider an extension of quantum mechanics to a five-dimensional space-time. By taking probability densities as being independent of the fifth dimension and that the effect of a coordinate transformation is just a traslation, we get a functional form for the state vector. So, the wave function results multiplied by a phase factor that could modify the outcoming of an interference experiment. By requiring the invariance of the interference pattern we get that the phase of the multiplying factor is quantized. To show a sample application, we apply the argument to the electric charge and consider the hypothesis that a pointlike object in ordinary four-dimensional space-time could have an extension in the fifth dimension.