Algebraic structure of classical integrability for complex sine-Gordon

Abstract

The algebraic structure underlying the classical rr-matrix formulation of the complex sine-Gordon model is fully elucidated. It is characterized by two matrices aa and ss, components of the rr matrix as r=a-sr=a−s. They obey a modified classical reflection/Yang–Baxter set of equations, further deformed by non-abelian dynamical shift terms along the dual Lie algebra su(2)^*su(2)*. The sign shift pattern of this deformation has the signature of the twisted boundary dynamical algebra. Issues related to the quantization of this algebraic structure and the formulation of quantum complex sine-Gordon on those lines are introduced and discussed.