Gauge Gravitational Field in a Fractal Space-Time

Considering the fractal structure of space-time, the scale relativity theory in the topological dimension D_T=2 is built. In such a conjecture, the geodesics of this space-time imply the hydrodynamic model of the quantum mechanics. Subsequently, the gauge gravitational field on a fractal space-time is given. Then, the gauge group, the gauge-covariantderivative, the strength tensor of the gauge field, the gauge-invariantLagrangean, the field equations of the gauge potentials and the gaugeenergy-momentum tensor are determined. Finally, using this model, aReissner-Nordström type metric is obtained.