Boundary Exchange Algebras and Scattering on the Half Line

Abstract

Some algebraic aspects of field quantization in space-time with boundaries are discussed. We introduce an associative algebra, whose exchange properties are inferred from the scattering processes in integrable models with reflecting boundary conditions on the half line. The basic properties of this algebra are established and the Fock representations associated with certain involutions are derived. We apply these results for the construction of quantum fields and for the study of scattering on the half line.

Enlarged version, to appear in Comm. Math. Phys. Tex file, macros included, no figures, 32 pages

References in corpus (13)

• Boundary energy and boundary states in integrable quantum field theories
• Factorized Scattering in the Presence of Reflecting Boundaries
• Bound State Boundary S-matrix of the sine-Gordon Model
• Supersymmetry in Boundary Integrable Models
• Deriving Boundary S Matrices
• Affine Toda Field Theory in the Presence of Reflecting Boundaries
• Fock Representations of Quantum Fields with Generalized Statistic
• The boundary sine-Gordon theory: classical and semi-classical analysis
• Aspects of affine Toda field theory on a half line
• Covariance Properties of Reflection Equation Algebras
• Quantum integrability in two-dimensional systems with boundary
• Bosonic Realization of Boundary Operators in $SU(2)$-invariant Thirring Model
• Fock Spaces with Reflection Condition and Generalized Statistics

Cited by in corpus (34)

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• Bosonization and Scale Invariance on Quantum Wires
• Quantum Fields on Star Graphs
• Junctions of anyonic Luttinger wires
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• Representations of reflection algebras
• Reflection-Transmission Algebras
• Spontaneous symmetry breaking in the gl(N)-NLS hierarchy on the half line
• Luttinger Liquid in Non-equilibrium Steady State
• Non-equilibrium Steady States of Quantum Systems on Star Graphs
• Classification of reflection matrices related to (super) Yangians and application to open spin chain models
• Quantum wire junctions breaking time reversal invariance
• Yangians, finite W-algebras and the Non Linear Schrodinger hierarchy
• Yangian symmetry in the Non Linear Schrodinger hierarchy
• On perturbative quantum field theory with boundary
• The Nonlinear Schrodinger Equation on the Half Line
• Quantum Fields on Star Graphs with Bound States at the Vertex
• Reflection-Transmission Quantum Yang-Baxter Equations
• Quantum Field Theory on Star Graphs
• Exact results for the one-dimensional many-body problem with contact interaction: Including a tunable impurity
• Solving the quantum non-linear Schrodinger equation with delta-type impurity
• Localization of Quantum Fields on Branes
• Off-critical Luttinger Junctions
• Quantization of the Nonlinear Schrodinger Equation on the Half Line
• Yangians and their applications
• Interplay between Zamolodchikov-Faddeev and Reflection-Transmission algebras
• Energy transmutation in nonequilibrium quantum systems
• Nonlinear Schrödinger equation on the half-line without a conserved number of solitons
• Local Fields on the Brane Induced by Nonlocal Fields in the Bulk
• Spontaneous symmetry breaking in the non-linear Schrodinger hierarchy with defect
• The Role of Initial Conditions in Presence of Extra Dimensions
• Quantum group symmetry of integrable systems with or without boundary
• Factorization in integrable systems with impurity
• Aspects of Finite Temperature Quantum Field Theory in a Black Hole Background