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

The constraints implied by analyticity in two-dimensional factorised S-matr ix theories are reviewed. Whenever the theory is not time-reversal invarian t, it is argued that the familiar condition of 'Real analyticity' for the S -matrix amplitudes has to be superseded by a different one known as 'Hermit ian analyticity'. Examples are provided of integrable quantum field theorie s whose (diagonal) two-particle S-matrix amplitudes are Hermitian analytic but not Real analytic. It is also shown that Hermitian analyticity is consi stent with the bootstrap equations and that it ensures the equivalence betw een the notion of unitarity in the quantum group approach to factorised S-m atrices and the genuine unitarity of the S-matrix. (C) 1999 Elsevier Scienc e B.V. All rights reserved.