On the f sum rule and its extensions

The f sum rule is derived in a nonrelativistic frame and connected, via Ward identities, to the two-photon term of the Compton 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 derived and provides nonperturbative results