Singular Behaviour of Electrons and of Composite Fermions in a Finite Effective Field

Abstract

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.