  We consider an isotropic Fermi liquid in two dimensions near the n=2
Pomeranchuk instability in the charge channel. The order parameter is a
quadrupolar stress tensor with two polarizations, longitudinal and transverse
to the quadrupolar momentum tensor. Longitudinal and transverse bosonic modes
are characterized by dynamical exponents z_parallel=3 and z_perp=2,
respectively. Previous studies have found that such a system exhibits
multiscale quantum criticality with two different energy scales omega ~
xi^{-z_{parallel,perp}}, where xi is the correlation length. We study the
impact of the multiple energy scales on the electron Green function. The
interaction with the critical z_parallel =3 mode is known to give rise to a
local self-energy that develops a non-Fermi liquid form, Sigma(omega) ~
omega^{2/3} for frequencies larger than the energy scale omega ~ xi^{-3}. We
find that the exchange of transverse z_perp=2 fluctuations leads to a
logarithmically singular renormalizations of the quasiparticle residue Z and
the vertex Gamma. We derive and solve renormalization group equations for the
flow of Z and Gamma and show that the system develops an anomalous dimension at
the nematic quantum-critical point (QCP). As a result, the spectral function at
a fixed omega and varying k has a non-Lorentzian form. Away from the QCP, we
find that the flow of Z is cut at the energy scale omega_{FL} ~ xi^{-1},
associated with the z=1 dynamics of electrons. The z_perp=2 energy scale, omega
~ xi^{-2}, affects the flow of Z only if one includes into the theory
self-interaction of transverse fluctuations.
