Coupling of Density and Spin Fluctuations to Quasiparticles in a Fermi Liquid

The general interaction between quasiparticles and particle-hole excitations in a neutral Fermi system at $T=0\mathrm{}$ is investigated. Density and spin-density fluctuations and collective modes are treated on an equal basis. Use is made of Ward identities to relate the vertex function $\Gamma$ to the quasiparticle self-energy $\Sigma$, and logarithmic corrections to the self-energy are obtained. The coefficients of the logarithmic terms are calculated analytically in terms of known Landau parameters.