AFFINE TODA FIELD-THEORY ON A HALF-LINE

The question of the integrability of real-coupling affine toda field t heory on a half-line is addressed. It is found, by examining low-spin conserved charges, that the boundary conditions preserving integrabili ty are strongly constrained. In particular, for the a(n) (n > 1) serie s of models there can be no free parameters introduced by the boundary condition; indeed the only remaining freedom (apart from choosing the simple condition partial derivative 1phi = 0), resides in a choice of signs. For a special case of the boundary condition, it is argued tha t the classical boundary bound state spectrum is closely related to a consistent set of reflection factors in the quantum field theory.