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

TL;DR

This paper compares Hermitian and Real analyticity in two-dimensional factorised S-matrix theories, highlighting the importance of Hermitian analyticity when time-reversal symmetry is broken and its consistency with unitarity.

Contribution

It introduces Hermitian analyticity as a necessary generalization of Real analyticity for non-time-reversal invariant theories and demonstrates its compatibility with bootstrap equations and unitarity.

Findings

Hermitian analyticity replaces Real analyticity in non-time-reversal invariant theories.

Hermitian analyticity is consistent with bootstrap equations.

Ensures equivalence between quantum group unitarity and genuine unitarity.

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invariant, it is argued that the familiar condition of `Real analyticity' for the S-matrix amplitudes has to be superseded by a different one known as `Hermitian analyticity'.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