Factorized scattering in the presence of reflecting boundaries

1993/04/27 by Andreas Fring, A. Fring, R. Köberle · 8 citations
Mathematics · Physics and Astronomy · #Affine transformation #Algebraic structures and combinatorial models #Computer science #Consistency (knowledge bases) #Field (mathematics) #Geometry #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Optics #Physics #Pure mathematics #Reflection (computer programming) #Scattering #Scattering theory #Set (abstract data type) #hep-th

paper · pdf · doi:10.1016/0550-3213(94)90229-1

published as Nucl.Phys.B421:159-172,1994 · 18p., USP-IFQSC/TH/93-06

arxiv created 1993/04/27 · openalex publication_date 1994/06/01 · arxiv updated 2011/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We formulate a general set of consistency requirements, which are expected to be satisfied by the scattering matrices in the presence of reflecting boundaries. In particular we derive an equivalent to the boostrap equation involving the W-matrix, which encodes the reflection of a particle off a wall. This set of equations is sufficient to derive explicit formulas for W, which we illustrate in the case of some particular affine Toda field theories.

Citations

• The inverse scattering method approach to the quantum Shabat-Mikhailov model
• Boundary conditions for integrable quantum systems
• Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models

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• Dynamical response functions in the quantum Ising chain with a boundary
• Reflection K-matrices for 19-vertex models
• On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary