Marginal Fermi-liquid theory proposed by Varma et al. is based on an assumption concerning the imaginary part of the polarization propagator. We investigate the consequence of this assumption paying full respect to the Ward-Takahashi identity, and find that the vertex corrections are of vital importance. We confirm the validity of the marginal Fermi-liquid picture at high energy scale, where only the lowest order logarithmic correction is important. However, our result at the low-energy region is radically different from the marginal Fermi liquid theory, in the sense that the quasi-particle mass, strength of its pole, and the jump in the momentum distribution all remain finite at the Fermi level. This means that the Varma et al. assumption does not break the Fermi-liquid picture, as far as the low-energy excitations are concerned.
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