  The difference between the electromagnetic self-energies of proton and
neutron can be calculated with the Cottingham formula, which expresses the
self-energies as an integral over the electroproduction cross
sections---provided the nucleon matrix elements of the current commutator do
not contain a fixed pole. We show that, under the same proviso, the subtraction
function occurring in the dispersive representation of the virtual Compton
forward scattering amplitude is determined by the cross sections. The
representation in particular leads to a parameter-free sum rule for the nucleon
polarizabilities. We evaluate the sum rule for the difference between the
electric polarizabilities of proton and neutron by means of the available
parameterizations of the data and compare the result with experiment.
