  We consider systems of non-relativistic, interacting electrons at finite
density and zero temperature in d = 2, 3, ... dimensions. Our main concern is
to characterize those systems that, under the renormalization flow, are driven
away from the Landau Fermi liquid (LFL) renormalization group fixed point. We
are especially interested in understanding under what circumstances such a
system is a Marginal Fermi liquid (MFL) when the dimension of space is greater
or equal than 2 . The interacting electron system is analyzed by combining
renormalization group (RG) methods with bosonization techniques. The RG
calculations are organized as a double expansion in the inverse scale
parameter, $\lambda^{-1} ,$ which is proportional to the width of the effective
momentum space around the Fermi surface and in the running coupling constant, $
g_\lambda , $ which measures the strength of electron interactions at
corresponding energy scales. Excluding a superconducting instability, the
system can be analyzed by means of bosonization. The RG and the underlying
perturbation expansion in powers of $ \lambda^{-1} $ serve to characterize the
approximations involved by bosonizing the system. We argue that systems with
short-range interactions flow to the LFL fixed point. Within the approximations
involved by bosonization, the same holds for systems with long-range,
longitudinal, density-density interactions. For electron systems interacting
via long-range, transverse, current-current interactions a deviation from LFL
behaviour is possible : the results of the bosonization calculation are
consistent with a MFL, if the exponent parametrizing the singularity of the
interaction potential in momentum space is greater than or equal to d-1.

Condensed Matter