Cantorian ε(∞) space-time in Cartan, de Broglie and field theories

Some implications of the Cantorian fractal space-time in the study of inertial motion of one and two material points were analyzed. The gravitational interaction mass in these systems depends on the intra and extragalactic diffusion coefficients. The analysis of fractal dimensions in a vortex street and of a superconducting pair showed that these physical objects can be considered as two dimensional projections of a higher-dimensional fractal string

Hydrodynamic formulation of scale relativity theory and unified superconductivity by means of a fractal string

In the frame of hydrodynamic formulation of scale relativity theory for a coherent quantum fluid, one shows that some parameters of high-temperature superconductors (critical field, critical current, pair breaking time, fluxoid, state density, gap energy, etc.) come from the non-differentiability of the quantum space-time. Then, the vortex streets (responsible for superconductivity by means of the in-phase lattice oscillations mechanism) and the anyons (responsible for superconductivity by means of the composite fermions mechanism) may be considered as two-dimensional projections of a higher-dimensional fractal string, which implies the existence of just one mechanism inducing type II superconductivity. © 2003 Elsevier Science B.V. All rights reserved