Dispersion relations provide a powerful tool to analyse the electromagnetic
form factors of the nucleon for all momentum transfers. Constraints from
meson-nucleon scattering data, unitarity, and perturbative QCD can be included
in a straightforward way. In particular, we include the 2pi, rho-pi, and KKbar
continua as independent input in our analysis and provide an error band for our
results. Moreover, we discuss two different methods to include the asymptotic
constraints from perturbative QCD. We simultaneously analyze the world data for
all four form factors in both the space-like and time-like regions and
generally find good agreement with the data. We also extract the nucleon radii
and the omega-NN coupling constants. For the radii, we generally find good
agreement with other determinations with the exception of the electric charge
radius of the proton which comes out smaller. The omega-NN vector coupling
constant is determined relatively well by the fits, but for the tensor coupling
constant even the sign can not be determined.Comment: 24 pages, 9 figure