= Solution
{c}
Within a stable normal <Fermi liquid>, the low-<energy> states are described by long-lived <Landau quasiparticles> and <holes> in a thin shell about the <Fermi surface>; the <Pauli exclusion principle> suppresses their decay. Expanding the <energy> about the equilibrium occupations gives the one-<quasiparticle> <dispersion relation> at first order and the interaction between occupation changes at second order, namely the <Landau quasiparticle energy functional>. For a smooth interaction, radial deviations in that interaction may be neglected at leading order, leaving its angular dependence; higher occupation terms contribute higher powers of the small shell thickness. Collective occupation deformations are included in the same description. The sufficiency claim is conditional on the normal <Fermi liquid> regime, and on supplementing this static <energy functional> with dynamics when required: it is not a description of arbitrary low-<energy> phases such as a <superconductor> or <non-Fermi liquid>.
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