Quantum integrability of certain boundary conditions

We study the quantum integrability of the O(N) Nonlinear σ (nlσ) model and the O(N) Gross-Neveu (GN) model on the half-line. We show that the nlσ model is integrable with Neumann, Dirichlet and a mixed boundary condition and that the GN model is integrable if ψ+a|x=0=±ψ−a|x=0. We also comment on the boundary condition found by Corrigan and Sheng for the O(3) nlσ model.