Boundary Yang-Baxter equation in the RSOS/SOS representation

Abstract

We construct and solve the boundary Yang-Baxter equation in the RSOS/SOS representation. We find two classes of trigonometric solutions; diagonal and non-diagonal. As a lattice model, these two classes of solutions correspond to RSOS/SOS models with fixed and free boundary spins respectively. Applied to (1+1)-dimenional quantum field theory, these solutions give the boundary scattering amplitudes of the particles. For the diagonal solution, we propose an algebraic Bethe ansatz method to diagonalize the SOS-type transfer matrix with boundary and obtain the Bethe ansatz equations.Comment: 30 pages, 5 figures, uses Latex with eepic.sty and epic.sty. Paper substantially expanded; section on SOS model is revised and a new section on the Bethe ansatz equation is adde