Affine Toda field theories related to Coxeter groups of noncrystallographic type

We propose affine Toda field theories related to the noncrystallographic Coxeter groups H2,H3 and H4. The classical mass spectrum, the classical three-point couplings and the one-loop corrections to the mass renormalisation are determined. The construction is carried out by means of a reduction procedure from crystallographic to noncrystallographic Coxeter groups. The embedding structure explains for various affine Toda field theories that their particles can be organised in pairs, such that their relative masses differ by the golden ratio.