BOSONIZATION AND THE EIKONAL EXPANSION - SIMILARITIES AND DIFFERENCES

We compare two non-perturbative techniques for calculating the single- particle Green's function of interacting Fermi systems with dominant f orward scattering: our recently developed functional integral approach to bosonization in arbitrary dimensions, and the eikonal expansion. I n both methods the Green's function is first calculated for a fixed co nfiguration of a background field, and then averaged with respect to a suitably defined effective action. We show that, after linearization of the energy dispersion at the Fermi surface, both methods yield for Fermi liquids exactly the same non-perturbative expression for the qua si-particle residue. However, in the case of non-Fermi liquid behavior the low-energy behavior of the Green's function predicted by the eiko nal method can be erroneous. In particular, for the Tomonaga-Luttinger model the eikonal method neither reproduces the correct scaling behav ior of the spectral function, nor predicts the correct location of its singularities.