Why normal electrons with sufficiently singular interactions do not have a sharp Fermi surface

We use a bosonization approach to show that the momentum distribution $n_{\bf{k}}$ of normal Fermi systems with sufficiently singular interactions is analytic in the vicinity of the non-interacting Fermi surface. These include singular density-density interactions that diverge in $d$ dimensions stronger than $| {\bf{q}} |^{- 2 (d -1)}$ for vanishing momentum transfer ${\bf{q}}$, but also fermions that are coupled to transverse gauge fields in $d < 3$.