Hermitian analyticity versus Real analyticity in two-dimensional factorised S-matrix theories

The constraints implied by analyticity in two-dimensional factorised S-matrix theories are reviewed. Whenever the theory is not time-reversal invariant, it is argued that the familiar condition of `Real analyticityʹ for the S-matrix amplitudes has to be superseded by a different one known as `Hermitian analyticityʹ. Examples are provided of integrable quantum field theories whose (diagonal) two-particle S-matrix amplitudes are Hermitian analytic but not Real analytic. It is also shown that Hermitian analyticity is consistent with the bootstrap equations and that it ensures the equivalence between the notion of unitarity in the quantum group approach to factorised S-matrices and the genuine unitarity of the S-matrix.