Classically integrable field theories with defects

Abstract

Some ideas and remarks are presented concerning a possible Lagrangian approach to the study of internal boundary conditions relating integrable fields at the junction of two domains. The main example given in the article concerns single real scalar fields in each domain and it is found that these may be free, of Liouville type, or of sinh-Gordon type.

11 pages. Based on a talk given at the 6th International Workshop on Conformal Field Theory and Integrable Systems, Landau Institute, Chernogolovka, 15-21 September, 2002. Two references corrected

References in corpus (12)

• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Classically integrable boundary conditions for affine Toda field theories
• Affine Toda field theory on a half line
• Factorized Scattering in the Presence of Reflecting Boundaries
• Scattering Theory and Correlation Functions in Statistical Models with a Line of Defect
• Bound State Boundary S-matrix of the sine-Gordon Model
• Statistical Models with a Line of Defect
• Scattering in the Presence of a Reflecting and Transmitting Impurity
• Aspects of affine Toda field theory on a half line
• Reflection factors and a two-parameter family of boundary bound states in the sinh-Gordon model
• On duality and reflection factors for the sinh-Gordon model
• From integrability to conductance, impurity systems

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