Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and General

Correlation functions of theSU(2)-invariant Thirring model with a boundary

Bo-Yu Hou, Kangjie Shi, Yanshen Wang, Wen‐Li Yang

Published Jan 7, 1997• 3 citations
Publisher

Abstract

Using the bosonization and oscillator expressions of bulk and boundary Zamolodchikov - Faddeev algebras, the correlators of Jost functions via operators are obtained in the case of SU(2)-invariant Thirring model with a boundary.
DOI
10.1088/0305-4470/30/1/018

Related papers

BOSONIC REALIZATION OF BOUNDARY OPERATORS IN SU(2)-INVARIANT THIRRING MODEL

LIU CHAO, Yanshen Wang, Wen‐Li Yang +2 more

Boundary operators and boundary states in the SU(2)-invariant Thirring model are considered from the point of view of bosonization and oscillator realizations of bulk and boundary Zamolodchikov-Faddeev algebras.

arXiv:hep-th/9503178•International Journal of Modern Physics A•Dec 20, 1995•4 citations

Smirnov-Type Integral Formulae for Correlation Functions of the Bulk/Boundary XXZ Model in the Anti-Ferromagnetic Regime

Yas-Hiro Quano

Integral solutions to the quantum Knizhnik-Zamolodchikov equations for the correlation functions of both the bulk and boundary XXZ models in the anti-ferromagnetic regime are presented. The difference equations can be derived from Smirnov-type master equations for correlation functions on the basis of the CTM bootstrap. Our integral solutions with an appropriate choice of the integral kernel reproduce the formulae previously obtained by using the bosonization of the vertex operators of the quantum affine algebra Uq ().

arXiv:hep-th/0104018•Progress of Theoretical Physics•Sep 1, 2002•1 citation

Correlation functions in conformal invariant stochastic processes

Francisco Castilho Alcaraz, Vladimir Rittenberg

We consider the problem of correlation functions in the stationary states of one-dimensional stochastic models having conformal invariance. If one considers the space dependence of the correlators, the novel aspect is that although one considers systems with periodic boundary conditions, the observables are described by boundary operators. From our experience with equilibrium problems one would have expected bulk operators. Boundary operators have correlators having critical exponents being half of those of bulk operators. If one studies the space-time dependence of the two-point function, one has to consider one boundary and one bulk operators. The Raise and Peel model has conformal invariance as can be shown in the spin 1/2 basis of the Hamiltonian which gives the time evolution of the system. This is an XXZ quantum chain with twisted boundary condition and local interactions. This Hamiltonian is integrable and the spectrum is known in the finite-size scaling limit. In the stochastic base in which the process is defined, the Hamiltonian is not local anymore. The mapping into an SOS model, helps to define new local operators. As a byproduct some new properties of the SOS model are conjectured. The predictions of conformal invariance are discussed in the new framework and compared with Monte Carlo simulations.

arXiv:1508.06968•Journal of Statistical Mechanics Theory and Experiment•Nov 13, 2015•8 citations

Form Factors and Correlation Functions

Giuseppe Mussardo

Abstract At the heart of a quantum field theory are the correlation functions of the various fields. In the case of integrable models, the correlators can be expressed in terms of the spectral series based on the matrix elements on the asymptotic states. These matrix elements, also known as form factors, satisfy a set of functional and recursive equations that can exactly solved in many cases of physical interest. Chapter 19 covers general properties of form factors, Faddeev–Zamolodchikov algebra, symmetric polynomials, kinematical and bound state poles, the operator space and kernel functions, the stress-energy tensor and vacuum expectation values and the Ising model in a magnetic field.

•Mar 26, 2020•0 citations

Form factors of SU(N) invariant Thirring model

Yoshihiro Takeyama

We obtain a new integral formula for solutions of the rational quantum Knizhnik-Zamolodchikov equation associated with Lie algebra sl_{N} at level zero. Our formula contains the integral representation of form factors of SU(N) invariant Thirring model constructed by F. Smirnov. We write down recurrence relations arising from the construction of the form factors. We check that the recurrence relations hold for the form factors of the energy momentum tensor.

arXiv:math-ph/0112025•Dec 13, 2001•0 citations

Analytical Bethe ansatz for the boundarySU(2)-invariant Thirring model

Yanshen Wang

The eigenvalue of the transfer matrices for the boundary invariant Thirring model and Bethe ansatz equation satisfied by quasimomenta are obtained by the analytical Bethe ansatz approach.

Journal of Physics A Mathematical and General•Apr 7, 2000•1 citation
Integral solutions to the quantum Knizhnik-Zamolodchikov equations for the correlation functions of both the bulk and boundary XXZ models in the anti-ferromagnetic regime are presented. The difference equations can be derived from Smirnov-type master equations for correlation functions on the basis of the CTM bootstrap. Our integral solutions with an appropriate choice of the integral kernel reproduce the formulae previously obtained by using the bosonization of the vertex operators of the quantum affine algebra Uq ().
We consider the problem of correlation functions in the stationary states of one-dimensional stochastic models having conformal invariance. If one considers the space dependence of the correlators, the novel aspect is that although one considers systems with periodic boundary conditions, the observables are described by boundary operators. From our experience with equilibrium problems one would have expected bulk operators. Boundary operators have correlators having critical exponents being half of those of bulk operators. If one studies the space-time dependence of the two-point function, one has to consider one boundary and one bulk operators. The Raise and Peel model has conformal invariance as can be shown in the spin 1/2 basis of the Hamiltonian which gives the time evolution of the system. This is an XXZ quantum chain with twisted boundary condition and local interactions. This Hamiltonian is integrable and the spectrum is known in the finite-size scaling limit. In the stochastic base in which the process is defined, the Hamiltonian is not local anymore. The mapping into an SOS model, helps to define new local operators. As a byproduct some new properties of the SOS model are conjectured. The predictions of conformal invariance are discussed in the new framework and compared with Monte Carlo simulations.
Abstract At the heart of a quantum field theory are the correlation functions of the various fields. In the case of integrable models, the correlators can be expressed in terms of the spectral series based on the matrix elements on the asymptotic states. These matrix elements, also known as form factors, satisfy a set of functional and recursive equations that can exactly solved in many cases of physical interest. Chapter 19 covers general properties of form factors, Faddeev–Zamolodchikov algebra, symmetric polynomials, kinematical and bound state poles, the operator space and kernel functions, the stress-energy tensor and vacuum expectation values and the Ising model in a magnetic field.