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

The Exact Quantum Sine-Gordon Field Equation and Other Non-Perturbative Results

H. Babujian, M. Karowski, Technische Univ. Berlin (Germany). Sonderforschungsbereich 288 -Differentialgeometrie und Quantenphysik

Published Jan 1, 1999• 12 citations
OpenAlex

Abstract

Using the methods of the "form factor program" exact expressions of all matrix elements are obtained for several operators of the quantum sine Gordon model: all powers of the fundamental bose field, general exponentials of it, the energy momentum tensor and all higher currents. It is found that the quantum sineGordon field equation holds with an exact relation between the "bare" mass and the renormalized mass. Also a relation for the trace of the energy momentum is obtained. The eigenvalue problem for all higher conserved charges is solved. All results are compared with Feynman graph expansions and full agreement is found. PACS: 11.10.-z; 11.10.Kk; 11.55.Ds Keywords: Integrable quantum field theory, Form factors The classical sine-Gordon model is given by the wave equation 2'(t; x) + ff fi sin fi'(t; x) = 0: Since Coleman [1] found the wonderful duality between the quantum sine-Gordon and the massive Thirring model a lot of effort has been made to understand this quantum field theo...

Related papers

Sine-Gordon breather form factors and quantum field equations

H. Babujian, M. Karowski

Using the results of previous investigations on sine-Gordon form factors, exact expressions of all breather matrix elements are obtained for several operators: all powers of the fundamental Bose field, general exponentials of it, the energy–momentum tensor and all higher currents. Formulae for the asymptotic behaviour of bosonic form factors are presented which are motivated by Weinberg's power counting theorem in perturbation theory. It is found that the quantum sine-Gordon field equation holds, and an exact relation between the 'bare' mass and the renormalized mass is obtained. Also a quantum version of a classical relation for the trace of the energy–momentum is proved. The eigenvalue problem for all higher conserved charges is solved. All results are compared with perturbative Feynman graph expansions and full agreement is found.

arXiv:hep-th/0204097•Journal of Physics A Mathematical and General•Oct 15, 2002•45 citations

ALGEBRAIC BETHE ANSATZ SCHEME FOR RELATIVISTIC INTEGRABLE FIELD THEORIES IN CONTINUUM-: SINE-GORDON MODEL

Gautam Bhattacharya, Sasanka Ghosh

The linear problem associated with the Lax operator of the classical sine-Gordon theory can be recast into the monodromy matrix form that can be extended to quantum theory as well. Product of the quantum monodromy matrices will have contributions from the singularities arising out of the operator product expansions of sine-Gordon field. This enables one to find the star-triangle relations. This is a generalization of the method used by Thacker for the non-relativistic nonlinear Schrödinger field theory. In the infinite volume limit, it leads to an unambiguous description of the algebra involving the scattering data operators. Starting from a vacuum the module of physical states are constructed by the application of chains of the scattering operators and they turn out to have definite eigenvalues of energy and momentum. The mass-spectra and two-particle S matrix elements can be calculated straightforwardly and they coincide with the well-known results of Zamolodchikov and Zamolodchikov. It is also shown that the particle states can be created by a generalized Jordon-Wigner transformation of the free fermionic creation operators — thus establishing a link between the S matrix element and certain co-cycles.

International Journal of Modern Physics A•Feb 1, 1989•6 citations

THE “BOOTSTRAP PROGRAM” FOR INTEGRABLE QUANTUM FIELD THEORIES IN 1 + 1 DIMENSIONS

H. Babujian, M. Karowski

The purpose of the "bootstrap program" is to construct integrable quantum field theories in 1+1 dimensions in terms of their Wightman functions explicitly. As an input the integrability and general assumptions of local quantum field theories are used. The object is to be achieved in tree steps: 1) The S-matrix is obtained using a qualitative knowledge of the particle spectrum and the Yang-Baxter equations. 2) Matrix elements of local operators are calculated by means of the "form factor program" using the S-matrix as an input. 3) The Wightman functions are calculated by taking sums over intermediate states. The first step has been performed for a large number of models and also the second one for several models. The third step is unsolved up to now. Here the program is illustrated in terms of the sine-Gordon model alias the massive Thirring model. Exploiting the "off-shell" Bethe Ansatz we propose general formulae for form factors. For example the n-particle matrix element for all higher currents are given and in particular all eigenvalues of the higher conserved charges are calculated. Furthermore quantum operator equations are obtained in terms of their matrix elements, in particular the quantum sine-Gordon field equation. Exact expressions for the finite wave function and mass renormalization constants are calculated.

arXiv:hep-th/0110261•WORLD SCIENTIFIC eBooks•Apr 1, 2002•9 citations

Lattice approach to finite volume form-factors of the Massive Thirring (Sine-Gordon) model

Árpád Hegedűs

In this paper we demonstrate, that the light-cone lattice approach for the Massive-Thirring (sine-Gordon) model, through the quantum inverse scattering method, admits an appropriate framework for computing the finite volume form-factors of local operators of the model. In this work we compute the finite volume diagonal matrix elements of the U(1) conserved current in the pure soliton sector of the theory. Based on the systematic large volume expansion of our results, we conjecture an exact expression for the finite volume expectation values of local operators in pure soliton states. At large volume in leading order these expectation values have the same form as in purely elastic scattering theories, but exponentially small corrections differ from previous Thermodynamic Bethe Ansatz conjectures of purely elastic scattering theories.

arXiv:1705.00319•Journal of High Energy Physics•Aug 1, 2017•6 citations

Lattice approach to finite volume form-factors of the Massive Thirring (Sine-Gordon) model

Árpád Hegedűs

In this paper we demonstrate, that the light-cone lattice approach for the Massive-Thirring (sine-Gordon) model, through the quantum inverse scattering method, admits an appropriate framework for computing the finite volume form-factors of local operators of the model. In this work we compute the finite volume diagonal matrix elements of the U(1) conserved current in the pure soliton sector of the theory. Based on the systematic large volume expansion of our results, we conjecture an exact expression for the finite volume expectation values of local operators in pure soliton states. At large volume in leading order these expectation values have the same form as in purely elastic scattering theories, but exponentially small corrections differ from previous Thermodynamic Bethe Ansatz conjectures of purely elastic scattering theories.

•Jan 1, 2017•7 citations

Thermodynamics of the Classical Massive-Thirring-Sine-Gordon Model

S. G. Chung

The proper classical limit $\ensuremath{\hbar}\ensuremath{\rightarrow}0$ of the quantum Bethe-Ansatz thermodynamics gives a new set of integral equations for the thermodynamics of the classical massive-Thirring-sine-Gordon model. The theory contains the thermodynamic information about breathers and solitons, and reproduces the transfer-matrix-method result for arbitrary coupling constant.

Physical Review Letters•Feb 13, 1989•11 citations
Using the methods of the "form factor program" exact expressions of all matrix elements are obtained for several operators of the quantum sine Gordon model: all powers of the fundamental bose field, general exponentials of it, the energy momentum tensor and all higher currents. It is found that the quantum sineGordon field equation holds with an exact relation between the "bare" mass and the renormalized mass. Also a relation for the trace of the energy momentum is obtained. The eigenvalue problem for all higher conserved charges is solved. All results are compared with Feynman graph expansions and full agreement is found. PACS: 11.10.-z; 11.10.Kk; 11.55.Ds Keywords: Integrable quantum field theory, Form factors The classical sine-Gordon model is given by the wave equation 2'(t; x) + ff fi sin fi'(t; x) = 0: Since Coleman [1] found the wonderful duality between the quantum sine-Gordon and the massive Thirring model a lot of effort has been made to understand this quantum field theo...
Using the results of previous investigations on sine-Gordon form factors, exact expressions of all breather matrix elements are obtained for several operators: all powers of the fundamental Bose field, general exponentials of it, the energy–momentum tensor and all higher currents. Formulae for the asymptotic behaviour of bosonic form factors are presented which are motivated by Weinberg's power counting theorem in perturbation theory. It is found that the quantum sine-Gordon field equation holds, and an exact relation between the 'bare' mass and the renormalized mass is obtained. Also a quantum version of a classical relation for the trace of the energy–momentum is proved. The eigenvalue problem for all higher conserved charges is solved. All results are compared with perturbative Feynman graph expansions and full agreement is found.
The linear problem associated with the Lax operator of the classical sine-Gordon theory can be recast into the monodromy matrix form that can be extended to quantum theory as well. Product of the quantum monodromy matrices will have contributions from the singularities arising out of the operator product expansions of sine-Gordon field. This enables one to find the star-triangle relations. This is a generalization of the method used by Thacker for the non-relativistic nonlinear Schrödinger field theory. In the infinite volume limit, it leads to an unambiguous description of the algebra involving the scattering data operators. Starting from a vacuum the module of physical states are constructed by the application of chains of the scattering operators and they turn out to have definite eigenvalues of energy and momentum. The mass-spectra and two-particle S matrix elements can be calculated straightforwardly and they coincide with the well-known results of Zamolodchikov and Zamolodchikov. It is also shown that the particle states can be created by a generalized Jordon-Wigner transformation of the free fermionic creation operators — thus establishing a link between the S matrix element and certain co-cycles.
The purpose of the "bootstrap program" is to construct integrable quantum field theories in 1+1 dimensions in terms of their Wightman functions explicitly. As an input the integrability and general assumptions of local quantum field theories are used. The object is to be achieved in tree steps: 1) The S-matrix is obtained using a qualitative knowledge of the particle spectrum and the Yang-Baxter equations. 2) Matrix elements of local operators are calculated by means of the "form factor program" using the S-matrix as an input. 3) The Wightman functions are calculated by taking sums over intermediate states. The first step has been performed for a large number of models and also the second one for several models. The third step is unsolved up to now. Here the program is illustrated in terms of the sine-Gordon model alias the massive Thirring model. Exploiting the "off-shell" Bethe Ansatz we propose general formulae for form factors. For example the n-particle matrix element for all higher currents are given and in particular all eigenvalues of the higher conserved charges are calculated. Furthermore quantum operator equations are obtained in terms of their matrix elements, in particular the quantum sine-Gordon field equation. Exact expressions for the finite wave function and mass renormalization constants are calculated.
In this paper we demonstrate, that the light-cone lattice approach for the Massive-Thirring (sine-Gordon) model, through the quantum inverse scattering method, admits an appropriate framework for computing the finite volume form-factors of local operators of the model. In this work we compute the finite volume diagonal matrix elements of the U(1) conserved current in the pure soliton sector of the theory. Based on the systematic large volume expansion of our results, we conjecture an exact expression for the finite volume expectation values of local operators in pure soliton states. At large volume in leading order these expectation values have the same form as in purely elastic scattering theories, but exponentially small corrections differ from previous Thermodynamic Bethe Ansatz conjectures of purely elastic scattering theories.
In this paper we demonstrate, that the light-cone lattice approach for the Massive-Thirring (sine-Gordon) model, through the quantum inverse scattering method, admits an appropriate framework for computing the finite volume form-factors of local operators of the model. In this work we compute the finite volume diagonal matrix elements of the U(1) conserved current in the pure soliton sector of the theory. Based on the systematic large volume expansion of our results, we conjecture an exact expression for the finite volume expectation values of local operators in pure soliton states. At large volume in leading order these expectation values have the same form as in purely elastic scattering theories, but exponentially small corrections differ from previous Thermodynamic Bethe Ansatz conjectures of purely elastic scattering theories.