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We consider the self-energy and quasiparticle spectrum, for both electronsinteracting with phonons, and composite fermions interacting with gaugefluctuations. In both cases we incorporate the singular structure arising fromLandau level quantization in a finite field. This is then used to determine therenormalised gap between the Fermi energy and the first excited states. Theelectron-phonon problem is treated for both Debye and Einstein phonons. In thecase of composite fermions, it is found that the singular Landau levelstructure strongly affects the renormalised gap in the intermediate couplingregime, which is relevant to experiments on the fractional quantum Hall effect.We compare our findings with measurements of the gap in fractional Hall stateswith filling fraction nu near nu=1/2.Comment: 13 pages including 11 figures, revte

Spectral Function Analysis of Fermi Liquids and of Composite Fermions in A Finite Magnetic Field: Renormalised Gaps