Kinks in the Kondo problem

We find the exact quasiparticle spectrum, elastic S matrix, and free energy for the continuum Kondo problem of k species of electrons coupled to an impurity of spin S. Here, the impurity becomes an immobile quasiparticle sitting on the boundary. The particles are ``kinks,'' which can be thought of as field configurations interpolating between adjacent wells of a potential with k+1 degenerate minima. For the overscreened case k>2S, the impurity in the continuum is a kink as well, which explains the noninteger number of boundary states.