Affine Toda Field Theory on a Half-line

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