= Solution
A normal <Fermi liquid> describes an interacting fermion system whose low-energy excitations remain continuously connected to adding particles to or removing particles from a <Fermi gas>. The elementary long-lived excitation is a <Landau quasiparticle>: adding a particle also changes the surrounding many-body state. Its <energy>, <velocity> and interactions are renormalized, even though its <electric charge> and <spin> remain those appropriate to the excitation.
Near an isotropic <Fermi surface>,
$$
\xi_{\mathbf k}=\varepsilon^*_{\mathbf k}-\mu\simeq\hbar v_F(k-k_F),\qquad m^*=\frac{\hbar k_F}{v_F}.
$$
Residual interactions make the <quasiparticle> <energy> depend on the occupations of other <quasiparticles>, expressed by the <Landau quasiparticle energy functional>. Its angular components give the <Landau parameters> controlling density and <spin> responses. Thus the successful particle picture does not mean that interactions have become zero.
Pauli blocking restricts the final states available for low-energy collisions. In an ordinary three-dimensional <Fermi liquid> with regular interactions, a representative decay law is
$$
\frac{\hbar}{\tau}=C\frac{\xi^2+(\pi k_BT)^2}{E_*},\qquad C>0.
$$
At $T=0$, the width vanishes faster than $|\xi|$, so an excitation becomes increasingly sharp as it approaches the <Fermi surface>. Its coherent spectral weight is the <quasiparticle residue> $Z$, and the physical <Electron> occupation has a discontinuity of height $Z$ at zero <temperature>. Incoherent spectral weight accounts for the remainder. The <quasiparticle> occupations themselves obey a <Fermi-Dirac distribution>.
Several leading thermodynamic signatures retain their gas-like form but have interaction-dependent coefficients. In particular,
$$
\frac{C_V}{\mathcal V}=\frac{\pi^2}{3}k_B^2N^*(0)T,\qquad \chi=\frac{\mu_0\mu_B^2N^*(0)}{1+F_0^a},\qquad \kappa=\frac{N^*(0)}{n^2(1+F_0^s)},
$$
for an isotropic spin-one-half model, with $N^*(0)$ the spin-summed <quasiparticle> <density of states> per volume. <effective mass> changes $N^*(0)$, while the dimensionless interaction parameters $F_0^a,F_0^s$ separately change the <spin> susceptibility and <compressibility>. Collisionless collective density motion can propagate as <zero sound>, distinct from the single-particle excitations.
The $T^2$ <quasiparticle> scattering rate often underlies a low-temperature $T^2$ contribution to metallic <electrical resistivity>, but a mechanism relaxing electrical <electric current> is needed. In a clean Galilean-invariant continuum, electron-electron collisions conserve total <momentum> and do not alone give a finite dc <electrical resistivity>. <Crystal> Umklapp scattering or other current-relaxing processes change that conclusion.
Normal liquid <helium-3> and many <metals> motivate the Fermi-liquid framework. Pairing, magnetic ordering or other transitions can reconstruct the low-energy states. Generic interacting one-dimensional fermion systems instead form a different low-energy state, so the three-dimensional <quasiparticle> conclusions should not simply be transferred to a chain.
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