  Re-studying the non-fermi liquid one-particle Green function (NFLGF) we have
extended the work of A. Balatsky (Phil. Mag. Lett. 68, 251 (1993)) and L. Yin
and S. Chakravarty (Int. J. Mod. Phys. B 10, 805 (1996)), among others. We used
the moment approach of W. Nolting (Z. Phys. 255, 25 (1972)) to compute the
unknown parameters of the NFLGF's in the framework of the Hubbard model. The
zeroth order momentum requires that our one-particle Green function describe
fermionic degrees of freedom. In order to satisfy the first order sum rule a
renormalization, $\gamma\neq 1$, of the free electron mass is called for. The
second order sum rule or moment imposes a relation between the non-Fermi liquid
parameter, $\alpha$, the Coulomb interaction, U, and the frequency cutoff,
$\omega_c$. We have calculated the effect of the mass renormalization factor,
$\gamma$, on some physical quantities. As a new class of non-Fermi liquid
systems, in Appendix A, we have studied two inequivalent coupled Hubbard layers
for which we calculated the one-particle spectral functions on the layers and
perpendicular to them. We discuss the new features which appear due to the
shift in the two effective chemical potentials and proposed some experiments to
detect the features founded from our expressions.
