  We develop two theoretical approaches for dealing with the low-energy effects
of the repulsive interaction in one-dimensional electron systems.
Renormalization Group methods allow us to study the low-energy behavior of the
unscreened interaction between currents of well-defined chirality in a strictly
one-dimensional electron system. A dimensional regularization approach is
useful, when dealing with the low-energy effects of the long-range Coulomb
interaction. This method allows us to avoid the infrared singularities arising
from the long-range Coulomb interaction at $D = 1$. We can also compare these
approaches with the Luttinger model, in order to analyze the effects of the
short range term in the interaction.
  Thanks to these methods, we are able to discuss the effects of a strong
magnetic field $B$ in quasi one-dimensional electron systems, by focusing our
attention on Carbon Nanotubes. Our results imply a variation with $B$ in the
value of the critical exponent $\alpha$ for the tunneling density of states,
which is in fair agreement with that observed in a recent transport experiment
involving carbon nanotubes. The dimensional regularization allows us to predict
the disappearance of the Luttinger liquid, when the magnetic field increases,
with the formation of a chiral liquid with $\alpha=0$.
