The Form Factor Program: a Review and New Results - the Nested SU(N) Off-Shell Bethe Ansatz

The purpose of the ''bootstrap program'' for integrable quantum field theories in 1+1 dimensions is to construct explicitly a model in terms of its Wightman functions. In this article, this program is mainly illustrated in terms of the sinh-Gordon model and the SU(N) Gross-Neveu model. The nested off-shell Bethe ansatz for an SU(N) factorizing S-matrix is constructed. We review some previous results on sinh-Gordon form factors and the quantum operator field equation. The problem of how to sum over intermediate states is considered in the short distance limit of the two point Wightman function for the sinh-Gordon model.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Exact form factors of the SU(N) Gross-Neveu model and 1/N expansion

The general SU(N) form factor formula is constructed. Exact form factors for the field, the energy momentum and the current operators are derived and compared with the 1/N-expansion of the chiral Gross-Neveu model and full agreement is found. As an application of the form factor approach the equal time commutation rules of arbitrary local fields are derived and in general anyonic behavior is found.Comment: 35 pages Published version of the paper, which includes minor corrections and improved acknowledgement

Bethe ansatz solution of a closed spin 1 XXZ Heisenberg chain with quantum algebra symmetry

A quantum algebra invariant integrable closed spin 1 chain is introduced and analysed in detail. The Bethe ansatz equations as well as the energy eigenvalues of the model are obtained. The highest weight property of the Bethe vectors with respect to U_q(sl(2)) is proved.Comment: 13 pages, LaTeX, to appear in J. Math. Phy

Exact form factors in integrable quantum field theories: the scaling Z(N)-Ising model

A general form factor formula for the scaling Z(N)-Ising model is constructed. Exact expressions for matrix elements are obtained for several local operators. In addition, the commutation rules for order, disorder parameters and para-Fermi fields are derived. Because of the unusual statistics of the fields, the quantum field theory seems to be not related to any classical Lagrangian or field equation.Comment: 36 page

Exact form factors of the O(N) σ-model

A general form factor formula for the O(N ) σ-model is constructed and applied to several operators. The large N limits of these form factors are computed and compared with the 1/N expansion of the O(N ) σ-model in terms of Feynman graphs and full agreement is found. In particular, O(3) and O(4) form factors are discussed. For the O(3) σ-model several low particle form factors are calculated explicitly

Exact form factors in integrable quantum field theories : the scaling Z(N)-ising model

A general form factor formula for the scaling Z(N)-Ising model is constructed. Exact expressions of all matrix elements are obtained for several local operators. In addition, the commutation rules for order, disorder parameters and para-Fermi fields are derived. Because of the unusual statistics of the fields, the quantum field theory seems not to be related to any classical Lagrangian or field equation

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

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

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

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