ASPECTS OF 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 discussed. It is shown, by examining low-spin conserved charges, that the boundary conditions preserving integrabili ty are strongly constrained. In particular, among the cases treated so far, e(6)(1), d(n)((1)) and a(n)((1)), n greater than or equal to 2, there can be no free parameters introduced by such boundary conditions ; indeed the only remaining freedom (apart from choosing the simple co ndition partial derivative(1) phi=0), resides in a choice of signs. Fo r a special case of the boundary condition, accessible only for a(n)(( 1)), it is pointed out that the classical boundary bound state spectru m may be related to a set of reflection factors in the quantum field t heory. Some preliminary calculations are reported for other boundary c onditions, demonstrating that the classical scattering data satisfies the weak coupling limit of the reflection bootstrap equation.