Discrete Space-Time by Means of the Weyl-Dirac Theory

A connection between the Weyl-Dirac theory and scale relativity theory through the hydrodynamic models (relativistic and non-relativistic approaches) is established. In such conjecture, considering that the motions of the microparticles take place on continuous but non-differentiable curves i.e. on fractals, a Weyl-Dirac type equation was found. Some correspondences with known hydrodynamic models, particularly Białynicki-Birula's approach, are analyzed. All these results reflect the fractal structure of the space-time (a concept in agreement with the new ideas on the space-time)