  We present a new step in the foundation of quantum field theory with the
tools of scale relativity. Previously, quantum motion equations (Schr\"odinger,
Klein-Gordon, Dirac, Pauli) have been derived as geodesic equations written
with a quantum-covariant derivative operator. Then, the nature of gauge
transformations, of gauge fields and of conserved charges have been given a
geometric meaning in terms of a scale-covariant derivative tool. Finally, the
electromagnetic Klein-Gordon equation has been recovered with a covariant
derivative constructed by combining the quantum-covariant velocity operator and
the scale-covariant derivative. We show here that if one tries to derive the
electromagnetic Dirac equation from the Klein-Gordon one as for the free
particle motion, i.e. as a square root of the time part of the Klein-Gordon
operator, one obtains an additional term which is the relativistic analog of
the spin-magnetic field coupling term of the Pauli equation. However, if one
first applies the quantum covariance, then implements the scale covariance
through the scale-covariant derivative, one obtains the electromagnetic Dirac
equation in its usual form. This method can also be applied successfully to the
derivation of the electromagnetic Klein-Gordon equation. This suggests it rests
on more profound roots of the theory, since it encompasses naturally the
spin-charge coupling.

General Physics;Quantum Physics