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

Free Field Representation and Form Factors of the Chiral Gross-Neveu Model

BRITTON, STEPHEN K, Sergey A. Frolov

Published Jan 1, 2013• 7 citations
OpenAlex

Abstract

The process of using the free field representation to construct form factors of two dimensional integrable models is very promising. In this thesis, this procedure is analysed and adapted for application to the chiral Gross-Neveu model. The vertex operators and Zamolodchikov-Faddeev algebra for the particles are presented, with a similar structure producing a representation of the local operators of the theory. Using these techniques, the form factors of the model are then constructed as traces over the space of Zamolodchikov-Faddeev operators, and given in terms of an integral representation. In particular, the two-particle form factors of the current operator are found, and shown to agree with previous results in the literature.

Related papers

Bethe Ansatz and exact form factors of the O (N) Gross Neveu-model

H. Babujian, Angela Foerster, Michael Karowski

We apply previous results on the O (N) Bethe Ansatz [1-3] to construct a general form factor formula for the O (N) Gross-Neveu model. We examine this formula for several operators, such as the energy momentum, the spin-field and the current. We also compare these results with the 1/N expansion of this model and obtain full agreement. We discuss bound state form factors, in particular for the three particle form factor of the field. In addition for the two particle case we prove a recursion relation for the K-functions of the higher level Bethe Ansatz.

arXiv:1510.08784•Journal of High Energy Physics•Feb 1, 2016•10 citations

Local Operators in Integrable Models I

Michio Jimbo, Tetsuji Miwa, Fedor Aleksandrovich Smirnov

ntegrable models in statistical mechanics and quantum field theory constitute a rich research field at the crossroads of modern mathematics and theoretical physics. An important issue to understand is the space of local operators in the system and, ultimately, their correlation functions and form factors. This book is the first published monograph on this subject. It treats integrable lattice models, notably the six-vertex model and the XXZ Heisenberg spin chain. A pair of fermions is introduced and used to create a basis of the space of local operators, leading to the result that all correlation functions at finite distances are expressible in terms of two transcendental functions with rational coefficients. Step-by-step explanations are given for all materials necessary for this construction, ranging from algebraic Bethe ansatz, representations of quantum groups, and the Bazhanov-Lukyanov-Zamolodchikov construction in conformal field theory to Riemann surfaces and their Jacobians. Several examples and applications are given along with numerical results.

Mathematical surveys and monographs•Jul 2, 2021•2 citations

Form factors of the O(6) Gross Neveu-model

Hrachya M. Babujian, Angela Foerster, Michael Karowski

The isomorphism $SU(4) \simeq O(6)$ is used to construct the form factors of the O(6) Gross-Neveu model as bound state form factors of the SU(4) chiral Gross-Neveu model. This technique is generalized and is then applied to use the O(6) as the starting point of the nesting procedure to obtain the O(N) form factors for general even N.

arXiv:1703.05973•Mar 17, 2017•1 citation

Bethe ansatz and exact form factors of the O (6) Gross Neveu-model *

H. Babujian, Angela Foerster, Michael Karowski

Abstract The isomorphism S U ( 4 ) ≃ O ( 6 ) is used to construct the form factors of the O ( 6 ) Gross–Neveu model as bound state form factors of the S U ( 4 ) chiral Gross–Neveu model. This technique is generalized and is then applied to use the O ( 6 ) as the starting point of the nesting procedure to obtain the O ( N ) form factors for general even N .

Journal of Physics A Mathematical and Theoretical•Jun 29, 2017•1 citation

Quantum Knizhnik-Zamolodchikov equation for Uq(sln) and integral formula

Takeo Kojima, Y -H Quano

An integral formula for solutions to the level-zero quantum Knizhnik-Zamolodchikov equation associated with the vector representation of U q (sl n ) is presented. This formula gives a generalization of both our previous work for U q (sl n ) and Smirnov's formula for form factors of the SU(n) chiral Gross-Neveu model.

arXiv:hep-th/9605123•Journal of Physics A Mathematical and General•Oct 21, 1994•4 citations

The Chiral Space of Local Operators in SU(2)-Invariant Thirring Model

Atsushi Nakayashiki

The space of local operators in the SU(2) invariant Thirring model (SU(2) ITM) is studied by the form factor bootstrap method. By constructing sets of form factors explicitly we define a susbspace of operators which has the same character as the level one integrable highest weight representation of ̂ sl2. This makes a correspondence between this subspace and the chiral space of local operators in the underlying conformal field theory, the su(2) Wess-Zumino-Witten model at level one. 1

•Jan 1, 2003•5 citations
The process of using the free field representation to construct form factors of two dimensional integrable models is very promising. In this thesis, this procedure is analysed and adapted for application to the chiral Gross-Neveu model. The vertex operators and Zamolodchikov-Faddeev algebra for the particles are presented, with a similar structure producing a representation of the local operators of the theory. Using these techniques, the form factors of the model are then constructed as traces over the space of Zamolodchikov-Faddeev operators, and given in terms of an integral representation. In particular, the two-particle form factors of the current operator are found, and shown to agree with previous results in the literature.
We apply previous results on the O (N) Bethe Ansatz [1-3] to construct a general form factor formula for the O (N) Gross-Neveu model. We examine this formula for several operators, such as the energy momentum, the spin-field and the current. We also compare these results with the 1/N expansion of this model and obtain full agreement. We discuss bound state form factors, in particular for the three particle form factor of the field. In addition for the two particle case we prove a recursion relation for the K-functions of the higher level Bethe Ansatz.
ntegrable models in statistical mechanics and quantum field theory constitute a rich research field at the crossroads of modern mathematics and theoretical physics. An important issue to understand is the space of local operators in the system and, ultimately, their correlation functions and form factors. This book is the first published monograph on this subject. It treats integrable lattice models, notably the six-vertex model and the XXZ Heisenberg spin chain. A pair of fermions is introduced and used to create a basis of the space of local operators, leading to the result that all correlation functions at finite distances are expressible in terms of two transcendental functions with rational coefficients. Step-by-step explanations are given for all materials necessary for this construction, ranging from algebraic Bethe ansatz, representations of quantum groups, and the Bazhanov-Lukyanov-Zamolodchikov construction in conformal field theory to Riemann surfaces and their Jacobians. Several examples and applications are given along with numerical results.
The isomorphism SU(4)≃O(6)SU(4) \simeq O(6)SU(4)≃O(6) is used to construct the form factors of the O(6) Gross-Neveu model as bound state form factors of the SU(4) chiral Gross-Neveu model. This technique is generalized and is then applied to use the O(6) as the starting point of the nesting procedure to obtain the O(N) form factors for general even N.