SPECTRAL-FUNCTION ANALYSIS OF FERMI LIQUIDS AND OF COMPOSITE FERMIONSIN A FINITE MAGNETIC-FIELD - RENORMALIZED GAPS

We consider the self-energy and quasiparticle spectrum, for both elect rons interacting with phonons, and composite fermions interacting with gauge fluctuations. :In both cases we incorporate the singular struct ure arising from Landau level quantization in a finite field. This is then used to determine the renormalised gap between the Fermi energy a nd the first excited states. The electron-phonon problem is treated fo r both Debye and Einstein phonons. In the case of composite fermions, it is found that the singular Landau level structure strongly affects the renormalised gap in the intermediate coupling regime, which is rel evant to experiments on the fractional quantum Hall effect. We compare our findings with measurements of the gap in fractional Hall states w ith filling fraction nu near nu = 1/2.