  We consider a system of 2D fermions with short-range interaction. A
straightforward perturbation theory is shown to be ill-defined even for an
infinitesimally weak interaction, as the perturbative series for the
self-energy diverges near the mass shell. We show that the divergences result
from the interaction of fermions with the zero-sound collective mode. By
re-summing the most divergent diagrams, we obtain a closed form of the
self-energy near the mass shell. The spectral function exhibits a threshold
feature at the onset of the emission of the zero-sound waves. We also show that
the interaction with the zero sound does not affect a non-analytic,
$T^{2}$-part of the specific heat.
