The Lagrangian density 
in electromagnetic interactions (EM) can
be written as:
where 
is the 4-vector potential. The interpretation of
as current follows from the fact that 
satisfies
the current conservation requirement. For illustration, consider an
electron-proton scattering. In one photon-exchange approximation, the
scattering amplitude is:
where the electron current takes the form:
and the proton current is written as:
is the fine structure constant; k, 
are the initial
and final 4-momenta of the electron; p,
the corresponding 4-momenta of the proton and q is the momentum
transferred:
is constructed from the proton 4-momenta and the
matrices. Due to Lorentz invariance and parity conservation
of EM interactions 
can only be vectors. Therefore, the hadronic
current is:
The quantities 
are functions of 
only because 
can be
expressed as a function of 
and the masses involved. Using the following
identities
and
the terms involving 
can be incorporated into other factors and
reduces to the following:
where 
is constant and M is the proton mass. The factor
is inserted to make 
coincide with the conventional
definition of the EM form factor. The current
conservation requirement leads to 
for elastic scattering (
).
The electric and magnetic form factors 
and 
can be
shown to be linear combinations of 
and 
. In
the non-relativistic limit, 
and 
are
interpreted as the
Fourier transforms of the charge and the magnetic moment distributions
inside the nucleus.
