Foundation of gauge fields theories on the principle of scale relativity

This article contains : 1. Introduction ; 2. Statement of the problem ; 3. The theory of scale relativity : summary ; 3.1 Principle of scale relativity ; 3.2 Galilean scale-relativity ; 3.3 Special scale-relativity ; 3.4 Relativistic quantum mechanics: Klein-Gordon equation ; 3.5 Dirac equation ; 3.6 Covariant tool : complex velocity operator ; 4. Classical electrodynamics in scale relativity ; 4.1 Scale-covariant derivative ; 4.2 Gauge invariance ; 4.3 Definition of the electric charge ; 4.4 Derivation of Lorentz force from geodesics equation ; 4.4.1 Generalized invariant proper time ; 4.4.2 Covariant derivative of a vector ; 4.4.3 Geodesics equation from covariance principle ; 4.4.4 Geodesics equation from energy equation ; 4.5 Link with Weyl-Dirac theory ; 5. Quantum electrodynamics ; 5.1 Introduction ; 5.2 QED-covariant derivative ; 5.3 Electromagnetic KG equation from a geodesics eqution ; 5.4 Nature of the electric charge (quantum theory) ; 5.5 Charge quantization and mass-coupling relations ; 6. Conclusion and future prospect . – References, 172-173. F. F.