= Fermi sea
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The Fermi sea is the zero-temperature many-<fermion> <quantum state> with every one-particle state below the <Fermi energy> occupied and every state above it empty. For a uniform isotropic <Fermi gas>, the occupied region in <momentum space> is a solid <sphere>; its boundary is the <Fermi surface>. These are <momenta>, not positions: filling the <sphere> does not put the particles in a ball in ordinary space. Opposite <momentum> contributions cancel, so the gas at rest has zero total <momentum> even though its total <kinetic energy> is positive.
The filled states are forced upward in <energy> by the <Pauli exclusion principle>. This is different from the <zero-point energy> of one particle confined by a boundary. At fixed <number density>, the <Fermi energy> remains positive as the box grows to the <thermodynamic limit>, while the lowest box confinement <energy> tends to zero. Low-<energy> excitations move particles from occupied states near the <Fermi surface> into nearby empty states; deep states have no nearby available destination. This explains why only a small fraction of <electrons> contribute to the low-<temperature> <electron heat capacity>.<Statistical Physics by David Tong/3 Quantum Gases>[Statistical Physics by David Tong; §§3.6.2–3.6.3, filled sea and thermally active surface shell]{ref}
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