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Exact Form Factors in Integrable Quantum Field Theories: the Sine-Gordon Model
High Energy Physics - Theory · Submitted 27 May 1998
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We carry out a consistency check for the solution of the three particle form factor against the Thirring model perturbation theory and thus confirm the general formalism.
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The abstract, sentence by sentence
We provide detailed arguments on how to derive properties of generalized form factors, originally proposed by one of the authors (M.K.) and Weisz twenty years ago, solely based on the assumption of "minimal analyticity" and the validity of the LSZ reduction formalism. These properties constitute consistency equations which allow the explicit evaluation of the n-particle form factors once the scattering matrix is known. The equations give rise to a matrix Riemann-Hilbert problem. Exploiting the "off-shell" Bethe ansatz we propose a general formula for form factors for an odd number of particles. For the Sine-Gordon model alias the massive Thirring model we exemplify the general solution for several operators. We carry out a consistency check for the solution of the three particle form factor against the Thirring model perturbation theory and thus confirm the general formalism.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We provide detailed arguments on how to derive properties of generalized form factors, originally proposed by one of the authors (M.K.) and Weisz twenty years ago, solely based on the assumption of "minimal analyticity" and the validity of the LSZ reduction formalism. | contribution 0.90 | 0.84 | 0.15 | asserted 1.00 |
| s1 | These properties constitute consistency equations which allow the explicit evaluation of the n-particle form factors once the scattering matrix is known. | result 0.58 | 0.52 | 0.25 | asserted 1.00 |
| s2 | The equations give rise to a matrix Riemann-Hilbert problem. | result 0.76 | 0.68 | 0.08 | asserted 1.00 |
| s3 | Exploiting the "off-shell" Bethe ansatz we propose a general formula for form factors for an odd number of particles. | contribution 0.67 | 0.92 | 0.20 | asserted 0.70 |
| s4 | For the Sine-Gordon model alias the massive Thirring model we exemplify the general solution for several operators. | contribution 0.84 | 0.90 | 0.12 | asserted 1.00 |
| s5 | We carry out a consistency check for the solution of the three particle form factor against the Thirring model perturbation theory and thus confirm the general formalism. | result 0.69 | 0.95 | 0.33 | asserted 1.00 |
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The paper
Original abstract
We provide detailed arguments on how to derive properties of generalized form factors, originally proposed by one of the authors (M.K.) and Weisz twenty years ago, solely based on the assumption of "minimal analyticity" and the validity of the LSZ reduction formalism. These properties constitute consistency equations which allow the explicit evaluation of the n-particle form factors once the scattering matrix is known. The equations give rise to a matrix Riemann-Hilbert problem. Exploiting the "off-shell" Bethe ansatz we propose a general formula for form factors for an odd number of particles. For the Sine-Gordon model alias the massive Thirring model we exemplify the general solution for several operators. We carry out a consistency check for the solution of the three particle form factor against the Thirring model perturbation theory and thus confirm the general formalism.
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References
How the literature uses it
27 arXiv papers cite this in 53 sentences
Papers citing it · 36 sentences without a confident label
Builds on it 1 paper
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This fusion table is the same as the restriction of the table of the Thirring model [ref] to the breather-breather sector (note that it is called “the sine-Gordon model” in the literature in the form factor programme, e.g. [ref] , assuming the equivalence between them).
Wedge-local observables in the deformed sine-Gordon model · Concluding remarks · 0.82
Uses its method or tool 1 paper
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In this article we will explore the crossing formula [ref] in order to start calculation of the multipoint Green functions or Wightman functions in 1+1 dimensional integrable quantum field theories.
Multipoint Green's functions in 1+1 dimensional integrable quantum field theories · Introduction · 0.84
Cites it as background 13 papers
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The second step is the form factor bootstrap, which uses the already calculated S-matrix to determine the matrix elements of local operators, from which the correlation functions can be built up [ref] .
Classical limit of diagonal form factors and HHL correlators · Introduction · 0.90
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Its exact form factors are also known in full generality [ref] , and so it is a useful playground to test our theoretical ideas on finite volume form factors.
Sine-Gordon multi-soliton form factors in finite volume · Introduction · 0.81
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At present, there are three independent constructions of solitonic form factors available: the earliest one by Smirnov (reviewed in [ref] ), the free field representation by Lukyanov [ref] and the work by Babujian et al. [ref] .
Sine-Gordon form factors in finite volume · Soliton form factors · 0.97
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