EXACT SOLUTION OF A MASSLESS SCALAR FIELD WITH A RELEVANT BOUNDARY INTERACTION

We solve exactly the ''boundary sine-Gordon'' system of a massless sca lar field phi with a cos(1/2 beta phi) potential at a boundary. This m odel has appeared in several contexts, including tunneling between qua ntum-Hall edge states and in dissipative quantum mechanics. For beta(2 ) < 8 pi, this system exhibits a boundary renormalization-group flow f rom Neumann to Dirichlet boundary conditions. By taking the massless l imit of the sine-Gordon model with boundary potential, we find the exa ct S-matrix for particles scattering off the boundary. Using the therm odynamic Bethe ansatz, we calculate the boundary entropy along the ent ire flow. We show how these particles correspond to wave packets in th e classical Klein-Gordon equation, thus giving a more precise explanat ion of scattering in a massless theory.