= Galilean boost energy of an interacting gas
{c}
{title2=$\Delta E=Np_0^2/(2m)$}
For a resting uniform continuum gas with pair interactions depending on relative positions, shifting every particle <momentum> by $\mathbf p_0$ leaves interaction <energy> unchanged and changes the microscopic <kinetic energy> by $\mathbf p_0\cdot\mathbf P/m+Np_0^2/(2m)$. The resting <ground state> has total <momentum> $\mathbf P=0$. The resulting boost <energy> uses the bare <mass> even in an interacting <Fermi liquid>; matching this with the <Landau quasiparticle energy functional> constrains its interaction kernel.
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