Yang-Baxter equation and reflection equations in integrable models

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.

21 pages, Latex, Lectures in Schladming school of theoretical physics (March 1995)

References in corpus (5)

• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Factorized Scattering in the Presence of Reflecting Boundaries
• Integrable XYZ Spin Chain with Boundaries
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Cited by in corpus (13)

• Integrable Boundary Conditions for the One-Dimensional Hubbard Model
• Integrable and Conformal Boundary Conditions for sl(2) A-D-E Lattice Models and Unitary Minimal Conformal Field Theories
• Solving and classifying the solutions of the Yang-Baxter equation through a differential approach. Two-state systems
• On Separation of Variables for Reflection Algebras
• Gauge Theory and Boundary Integrability
• Matrix product solution to the reflection equation associated with a coideal subalgebra of $U_q(A_{n-1}^{(1)})$
• Set-theoretical solutions to the reflection equation associated to the quantum affine algebra of type $A_{n-1}^{(1)}$
• Reflection matrices with $U_q[os{p}^{(2)}(2|2m)]$ symmetry
• Connection problems for quantum affine KZ equations and integrable lattice models
• Matrix product solutions to the $G_2$ reflection equation
• Bethe/Gauge Correspondence for $A_N$ Spin Chains with Integrable Boundaries
• BC-type open $SL(2,\mathbb{C})$ spin chain
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish