  Using a precise coset Ising-Bose representation, we show how backscattering
of electrons off a magnetic impurity destabilizes the two-channel Kondo fixed
point and drives the system to a new fixed point, in agreement with previous
results. In addition, we verify the scaling proposed by Furusaki and Nagaosa
and prove that the other possible critical fixed point, namely the local Fermi
liquid class, is not completely universal when backscattering is included
because the Wilson ratio is not well-defined in the spinon basis.
