MASS FORMULAE IN TODA FIELD THEORIES

The characteristic equations which give the mass spectrum of the affine Toda field theories are analyzed. In order to determine the decoupling point of the finite renormalization due to the tadpoles we introduce the so-called mass formulae. We derive the recursive equations the mass formulae satisfy and study their properties for all Lie algebras. For the ADE series the mass formulae turn out to be sequences of integers.