DERIVING BOUNDARY S-MATRICES

We show how to derive exact boundary S matrices for integrable quantum field theories in 1 + 1 dimensions using lattice regularization. We d o this calculation explicitly for the sine-Gordon model with fixed bou ndary conditions using the Bethe ansatz for an XXZ-type spin chain in a boundary magnetic field. Our results agree with recent conjectures o f Ghoshal and Zamolodchikov, and indicate that the only solutions to t he Bethe equations which contribute to the scaling limit are the stand ard strings.