scholarly journals A NEW SET OF EXACT FORM FACTORS

1994 ◽  
Vol 09 (29) ◽  
pp. 5121-5143 ◽  
Author(s):  
FEODOR A. SMIRNOV
Keyword(s):  
Field Model ◽  
Central Charge ◽  
Form Factors ◽  
Present Form ◽  
Integrable Models ◽  
Chiral Field ◽  
Exact Form ◽  
Principal Chiral Field ◽  
Wide Range ◽  
Interesting Structure

We present form factors for a wide range of integrable models which include marginal perturbations of the SU(2) WZNZ model for arbitrary central charge and the principal chiral field model. The interesting structure of these form factors is discussed.

scholarly journals Form Factors for Principal Chiral Field Model with Wess–Zumino–Novikov–Witten Term

1997 ◽  
Vol 12 (19) ◽  
pp. 3383-3395 ◽  
Author(s):  
P. Mejean ◽  
F. A. Smirnov
Keyword(s):  
Ising Model ◽  
Field Model ◽  
Energy Momentum Tensor ◽  
Form Factors ◽  
Momentum Tensor ◽  
Chiral Field ◽  
Principal Chiral Field ◽  
Level 1

We construct the form factors of the trace of energy–momentum tensor for the massless model described by SU(2) principal chiral field model with WZNW term on level 1. We explain how this construction can be generalized to a class of integrable massless models including the flow from tricritical to critical Ising model. From F. Smirnov. During several months I worked with Pierre Mejean. After his premature decease which deeply affected everybody who knew him I decided to collect and to publish the results which we obtained together.

Integrability of the principal chiral field model in 1 + 1 dimension

1986 ◽  
Vol 167 (2) ◽  
pp. 227-256 ◽  
Author(s):  
L.D Faddeev ◽  
N.Yu Reshetikhin
Keyword(s):  
Field Model ◽  
Chiral Field ◽  
Principal Chiral Field

scholarly journals Approaching the self-dual point of the sinh-Gordon model

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Robert Konik ◽  
Márton Lájer ◽  
Giuseppe Mussardo
Keyword(s):  
Small Volume ◽  
Zero Mode ◽  
Form Factors ◽  
Lagrangian Formulation ◽  
The Self ◽  
Quantum Mechanical ◽  
Exact Form ◽  
Coupling Constant ◽  
Self Duality ◽  
Hyperbolic Cosine

Abstract One of the most striking but mysterious properties of the sinh-Gordon model (ShG) is the b → 1/b self-duality of its S-matrix, of which there is no trace in its Lagrangian formulation. Here b is the coupling appearing in the model’s eponymous hyperbolic cosine present in its Lagrangian, cosh(bϕ). In this paper we develop truncated spectrum methods (TSMs) for studying the sinh-Gordon model at a finite volume as we vary the coupling constant. We obtain the expected results for b ≪ 1 and intermediate values of b, but as the self-dual point b = 1 is approached, the basic application of the TSM to the ShG breaks down. We find that the TSM gives results with a strong cutoff Ec dependence, which disappears according only to a very slow power law in Ec. Standard renormalization group strategies — whether they be numerical or analytic — also fail to improve upon matters here. We thus explore three strategies to address the basic limitations of the TSM in the vicinity of b = 1. In the first, we focus on the small-volume spectrum. We attempt to understand how much of the physics of the ShG is encoded in the zero mode part of its Hamiltonian, in essence how ‘quantum mechanical’ vs ‘quantum field theoretic’ the problem is. In the second, we identify the divergencies present in perturbation theory and perform their resummation using a supra-Borel approximate. In the third approach, we use the exact form factors of the model to treat the ShG at one value of b as a perturbation of a ShG at a different coupling. In the light of this work, we argue that the strong coupling phase b > 1 of the Lagrangian formulation of model may be different from what is naïvely inferred from its S-matrix. In particular, we present an argument that the theory is massless for b > 1.

scholarly journals The nestedSU(N) off-shell Bethe ansatz and exact form factors

2008 ◽  
Vol 41 (27) ◽  
pp. 275202 ◽  
Author(s):  
H Babujian ◽  
A Foerster ◽  
M Karowski
Keyword(s):  
Bethe Ansatz ◽  
Form Factors ◽  
Exact Form

CORRELATION FUNCTIONS OF INTEGRABLE 2D MODELS OF THE RELATIVISTIC FIELD THEORY: ISING MODEL

1991 ◽  
Vol 06 (19) ◽  
pp. 3419-3440 ◽  
Author(s):  
V.P. YUROV ◽  
AL. B. ZAMOLODCHIKOV
Keyword(s):  
Magnetic Field ◽  
Correlation Functions ◽  
Form Factors ◽  
Field Theories ◽  
Scattering Data ◽  
Exact Form ◽  
Relativistic Field ◽  
Spin Correlations ◽  
Ising Spin ◽  
Infinite Sums

A program is proposed to study numerically the correlation functions in massive integrable 2D relativistic field theories. It relies crucially on the exact form factors of fields which can be reconstructed from the factorized scattering data. The correlation functions are expressible as infinite sums over intermediate asymptotic states. We suggest using computer power to perform the summation numerically. The convergence of the sum is tested for the simplest example of the scaling Ising spin-spin correlations (without magnetic field).

Method of separated form factors for polydisperse vesicles

2006 ◽  
Vol 39 (3) ◽  
pp. 293-303 ◽  
Author(s):  
Jeremy Pencer ◽  
Susan Krueger ◽  
Carl P. Adams ◽  
John Katsaras
Keyword(s):  
Form Factor ◽  
Laplace Transform ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Scattering Length ◽  
Form Factors ◽  
Particle Sizes ◽  
Exact Form ◽  
The Laplace Transform ◽  
Spherical Vesicles

Use of the Schulz or Gamma distribution in the description of particle sizes facilitates calculation of analytic polydisperse form factors using Laplace transforms, {\cal L}[f(u)]. Here, the Laplace transform approach is combined with the separated form factor (SFF) approximation [Kiselevet al.(2002).Appl. Phys. A,74, S1654–S1656] to obtain expressions for form factors,P(q), for polydisperse spherical vesicles with various forms of membrane scattering length density (SLD) profile. The SFF approximation is tested against exact form factors that have been numerically integrated over the size distribution, and is shown to represent the vesicle form factor accurately for typical vesicle sizes and membrane thicknesses. Finally, various model SLD profiles are used with the SFF approximation to fit experimental small-angle neutron scattering (SANS) curves from extruded unilamellar vesicles.

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