  We calculate the self-energy of fermions in Landau level n, in a finite
field. Two cases are considered, in which fermions couple either to gauge
fluctuations (as in the composite fermion gauge theory) or to phonons, as an
example of a Fermi liquid. Perturbative calculations of the composite fermion
spectrum show an unphysical suppression of the quasiparticle spectral weight at
the composite fermion levels. We argue that this problem might be resolved by a
non-perturbative calculation; alternatively, the system might be unstable.
