Yang-Baxter equation and reflection equations in integrable models

TL;DR

This paper reviews the foundational concepts of the quantum inverse scattering method, deriving the Yang-Baxter and reflection equations as key consistency conditions for integrable models on lines and half-lines.

Contribution

It introduces face model analogues of the Zamolodchikov-Faddeev algebra and reflection equations, including graded and colored algebra forms.

Findings

Derivation of Yang-Baxter and reflection equations from consistency conditions

Introduction of face model analogues of ZF algebra and reflection equations

Presentation of graded and colored algebra forms of YBE and RE

Abstract

The definitions of the main notions related to the quantum inverse scattering methods are given. The Yang-Baxter equation and reflection equations are derived as consistency conditions for the factorizable scattering on the whole line and on the half-line using the Zamolodchikov-Faddeev algebra. Due to the vertex-IRF model correspondence the face model analogue of the ZF-algebra and the IRF reflection equation are written down as well as the $Z_2$-graded and colored algebra forms of the YBE and RE.