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

Abstract

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invariant, it is argued that the familiar condition of `Real analyticity' for the S-matrix amplitudes has to be superseded by a different one known as `Hermitian analyticity'. 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.

9 pages, LaTeX file. The comments about unitarity in affine Toda theories have been improved. The basis dependence of the Hermitian analyticity conditions is discussed

References in corpus (4)

• Solitonic Integrable Perturbations of Parafermionic Theories
• Semi-classical spectrum of the Homogeneous sine-Gordon theories
• ${\Phi }^{(2)}$ Perturbations of WZW Model
• The R-matrix of the U_q(d_4(3)) algebra and g_2(1) affine Toda field theory

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• Lectures on S-matrices and Integrability
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• Effective Field Theories as Lagrange Spaces
• RSOS revisited
• Supersymmetric integrable scattering theories with unstable particles
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