  The Kondo effect in a Luttinger liquid is studied using the renormalization
group method. By renormalizing the boson fields, scaling equations to the
second order for an arbitrary Luttinger interaction are obtained. For the
ferromagnetic Kondo coupling, a spin bound state(triplet) can be realized
without invoking a nearest neighbor spin interaction in agreement with the
recent Bethe ansatz calculation. The scaling theory in the presence of the
scalar potential shows that there is no interplay between the magnetic and
non-magnetic interaction. Also a study on the crossover behavior of the Kondo
temperature between the exponential and the power law type is presented.
