  Tunneling through a localized barrier in a one-dimensional interacting
electron gas has been studied recently using Luttinger liquid techniques.
Stable phases with zero or unit transmission occur, as well as critical points
with universal fractional transmission whose properties have only been
calculated approximately, using a type of ``$\epsilon$-expansion''. It may be
possible to calculate the universal properties of these critical points exactly
using the recent boundary conformal field theory technique, although
difficulties arise from the $\infty$ number of conformal towers in this $c=4$
theory and the absence of any apparent ``fusion'' principle. Here, we formulate
the problem efficiently in this new language, and recover the critical
properties of the stable phases.
