Reflection-Transmission Algebras

Abstract

Inspired by factorized scattering from delta-type impurities in (1+1)-dimensional space-time, we propose and analyse a generalization of the Zamolodchikov-Faddeev algebra. Distinguished elements of the new algebra, called reflection and transmission generators, encode the particle-impurity interactions. We describe in detail the underlying algebraic structure. The relative Fock representations are explicitly constructed and a general factorized scattering theory is developed in this framework.

LaTex, 34 pages, 4 figures

References in corpus (17)

• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Holography and Defect Conformal Field Theories
• Permeable conformal walls and holography
• Factorized Scattering in the Presence of Reflecting Boundaries
• Scattering Theory and Correlation Functions in Statistical Models with a Line of Defect
• Purely Transmitting Defect Field Theories
• Scattering in the Presence of a Reflecting and Transmitting Impurity
• Fock Representations of Quantum Fields with Generalized Statistic
• Aspects of affine Toda field theory on a half line
• Boundary Exchange Algebras and Scattering on the Half Line
• Spontaneous symmetry breaking in the gl(N)-NLS hierarchy on the half line
• On the absence of simultaneous reflection and transmission in integrable impurity systems
• From integrability to conductance, impurity systems
• Small-Size Instanton Corrections to the $\tau$ Hadronic Width
• The Nonlinear Schrodinger Equation on the Half Line
• Higher Level Open String States from Vacuum String Field Theory
• Quantization of the Nonlinear Schrodinger Equation on the Half Line

Cited by in corpus (39)

• Bosonization and Scale Invariance on Quantum Wires
• Junctions of anyonic Luttinger wires
• Quantum Fields on Star Graphs
• From Defects to Boundaries
• Liouville integrable defects: the non-linear Schrodinger paradigm
• Luttinger Liquid in Non-equilibrium Steady State
• Non-equilibrium Steady States of Quantum Systems on Star Graphs
• The quantum non-linear Schrodinger model with point-like defect
• A multisymplectic approach to defects in integrable classical field theory
• Quantum wire junctions breaking time reversal invariance
• Quantum Fields on Star Graphs with Bound States at the Vertex
• Sigma models in the presence of dynamical point-like defects
• Reflection-Transmission Quantum Yang-Baxter Equations
• Quantum Field Theory on Star Graphs
• Finite propagation speed and causal free quantum fields on networks
• Exact results for the one-dimensional many-body problem with contact interaction: Including a tunable impurity
• Direct computation of scattering matrices for general quantum graphs
• Solving the quantum non-linear Schrodinger equation with delta-type impurity
• Finite Temperature Quantum Field Theory with Impurities
• Multisymplectic approach to integrable defects in the sine-Gordon model
• Quantum field theory on quantum graphs and application to their conductance
• Classical impurities associated to high rank algebras
• Off-critical Luttinger Junctions
• Network Models: Action formulation
• Interplay between Zamolodchikov-Faddeev and Reflection-Transmission algebras
• Algebraic approach to multiple defects on the line and application to Casimir force
• Quantum Field Theories and Critical Phenomena on Defects
• Energy transmutation in nonequilibrium quantum systems
• Jumps and twists in affine Toda field theories
• Type-I integrable quantum impurities in the Heisenberg model
• Transmission matrices in gl(N) & U_q(gl(N)) quantum spin chains
• Nonlinear Schrödinger equation on the half-line without a conserved number of solitons
• A note on gl_N type-I integrable defects
• Spontaneous symmetry breaking in the non-linear Schrodinger hierarchy with defect
• Commuting quantum traces: the case of reflection algebras
• Exact scattering matrix of graphs in magnetic field and quantum noise
• Lax pair formulation in the simultaneous presence of boundaries and defects
• The sine-Gordon model in the presence of defects
• Factorization in integrable systems with impurity