Irreducible particle-hole

The pair scattering for two quasiparticles with opposite momenta at the Fermi surface is evaluated adopting the ladder approximation displayed in fig. 5. The problem is therefore reduced to finding the four-point vertex which is irreducible with respect to particle-particle scattering. The basic assumption is that the important structure in the scattering amplitudes comes from exchange of collective modes in the two particle-hole channels. The central quantity of these theories is the dynamic magnetic susceptibility x (fl ) which can be determined... 

This irreducible e-h interaction, via a Ward identity, also determines the particle-hole interaction in the Bethe-Salpeter equation (2.7) for the two-particle propagator. Ideally, we should... 

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