  The $f$ sum rule is derived in a non-relativistic frame and connected, via
Ward Identities, to the low energy Thomson scattering. A generalisation to
isospin symmetry in the nuclear case is discussed and linked to the Meson
Exchange Currents. The extension to a fully relativistic theory is then
discussed and it is shown that the energy-weighted sum rule becomes a relation
between the particle-hole and particle-antiparticle emission. Moreover the
generalisation to isospin symmetry is also allowed and provides
non-perturbative results.
