= Solution
A normal <Fermi liquid> has interacting fermions whose low-energy excitations can be followed continuously from those of a <Fermi gas>, provided no phase transition destroys that correspondence. A <Landau quasiparticle> is a particle together with the surrounding many-body response. It has the appropriate charge and <spin>, a renormalized dispersion and a long lifetime close to the <Fermi surface>. Interactions remain in both the <quasiparticle> parameters and the interactions between <quasiparticles>; they have not been discarded.
Near an isotropic <Fermi surface>,
$$
\xi_{\mathbf k}=\varepsilon^*_{\mathbf k}-\mu\simeq\hbar v_F(k-k_F),\qquad v_F=\frac1\hbar\left.\frac{\partial\varepsilon^*_{\mathbf k}}{\partial k}\right|_{k_F},\qquad m^*=\frac{\hbar k_F}{v_F}.
$$
The last relation defines the local isotropic <Fermi-liquid effective mass>. The <Landau quasiparticle energy functional> expresses how changing occupations shifts other <quasiparticle> energies:
$$
\delta\varepsilon^*_{\mathbf k\sigma}=\sum_{\mathbf k'\sigma'}f_{\mathbf k\sigma,\mathbf k'\sigma'}\delta n_{\mathbf k'\sigma'},
$$
with normalization of the sum absorbed into $f$. Its angular components give <Landau parameters> describing collective density and <spin> response.
The <Pauli exclusion principle> severely restricts the available final states for low-energy collisions. In an ordinary three-dimensional <Fermi liquid> with regular interactions,
$$
\boxed{\tau^{-1}\propto\xi^2+(\pi k_BT)^2.}
$$
At zero <temperature> the decay width decreases faster than $|\xi|$, making <quasiparticles> increasingly sharp near the <Fermi surface>. Their coherent spectral weight is the <quasiparticle residue> $0<Z\leq1$, and the true <Electron> <momentum> distribution has a discontinuity of height $Z$ at zero <temperature>. The rest of the spectral weight is incoherent. The <quasiparticle> occupation itself still follows a <Fermi-Dirac distribution>.
The low-temperature electronic <heat capacity> is linear, $C_V/\mathcal V=(\pi^2/3)k_B^2N^*(0)T$, where $N^*(0)$ is the spin-summed <quasiparticle> <density of states>. In an isotropic spin-one-half model, the uniform <spin> susceptibility and <compressibility> take the forms
$$
\chi=\frac{\mu_0\mu_B^2N^*(0)}{1+F_0^a},\qquad \kappa=\frac{N^*(0)}{n^2(1+F_0^s)}.
$$
Thus enhanced effective mass and residual interactions can separately change observable responses. The familiar $T^2$ <electrical resistivity> requires a mechanism relaxing electrical current, such as allowed Umklapp processes; collisions in a perfectly clean Galilean-invariant continuum conserve total <momentum> and do not alone produce a finite dc resistivity.
<Zero sound> is a collisionless collective density <oscillation> sustained by the <quasiparticle> interaction; ordinary first sound occurs when collisions establish local equilibrium during a cycle. Metals and normal liquid <helium-3> supply important examples. The description fails in phases with no sufficiently sharp low-energy <quasiparticles>, such as generic interacting one-dimensional systems, and must be modified after pairing or another ordering transition.
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