Principal Chiral Field Research Articles

The principal chiral field in two dimensions on classical lie algebras: The Bethe-ansatz solution and factorized theory of scattering

The Bethe-ansatz solution, the exact factorized complete S-matrix and the particle spectrum for a two-dimensional chiral field on principal manifolds associated with the classical Lie groups SU( k + 1), SO(2 k), SO(2 k + 1), Sp(2 k) are presented. It is shown that the elementary particles are massive and form the basis of the ring of representations of the diagonal of the direct product G × G. The exact results are obtained in the framework of both the Bethe-ansatz approach and the factorized bootstrap program. The bootstrap properties of the S-matrices and relations between the simple roots of the algebras and the solution are discussed.

Factorised S-matrix with G2symmetry

The solution of the factorisation equation possessing G2 symmetry is found in a 7D representation. Bootstrap properties of massive particles of the principal chiral field with G2 symmetry and the particle spectrum are discussed on the basis of the deduced solution.

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

The quantum inverse scattering method is used to solve model of the principal chiral field in 1 + 1 dimension. A different approach based on fermionization was proposed before by A. M. Polyakov and P. B. Wiegmann ( Phys. Lett. B 131 (1981), 121) . The main idea of our work is to get the relativistic model from the lattice magnetic model in the scaling limit with spin S going to infinity. Our method became realistic after the new Hamiltonian interpretation of the Pohlmeyer-Zakharov-Mikhailov L-M pair, ( K. Pohlmeyer, Comm. Math. Phys. 46 (1976), 207 ; V. E. Zakharov and A. V. Mikhailov, Sov. Phys. JETP (Engl. Transl.) 47 (1978), 1017 ) was devised.

Hamiltonian structures for integrable classical theories from graded Kac-Moody algebras

An infinite number of canonical representations for integrable classical field theories of non-ultralocal type are constructed from graded Kac-Moody algebras. The principal chiral field models are shown to be a particular example of this construction.

Heisenberg magnet with an arbitrary spin and anisotropic chiral field

The integrable generalization of the XXZ Heisenberg chain for an arbitrary spin s has been made on the basis of the U(1)-invariant solution of the Yang-Baxter equation. The thermodynamics of this magnetic system has been investigated. Using the same solution of the Yang-Baxter equation the integrable relativistic fermion model has been built which possesses the SU(2) × U(1) invariant two-particle scattering matrix. We provide some arguments to demonstrate the equivalence of this fermionic model and the model of the principal chiral field with a broken SU(2) symmetry. The Gell-Mann-Low function of the anisotropic chiral field has been analysed.

Gauge covariant formulation of integrability properties of symmetric-space fields

Integrability properties of symmetric-space chiral fields, principal chiral fields, and self-dual Yang-Mills fields are discussed in the gauge covariant form. The properties of the general Riccati equation for chiral fields are analyzed in some details.

Gauge covariant formulation of symmetric-space fields

For fields taking value in the symmetric space G/H, we give a general G gauge covariant formulation, and explicit vertical and horizontal decomposition of the Cartan-Mauerer relation in arbitrary gauges. From such explicit construction we show that a “zero”-gauge can be chosen for all symmetric-space fields so that the Cartan-Maurer conditions are automatically satisfied and the equations of motion become the only equations for the fields N( x), with N 2( x) = 1, Tr N( x) given. explicit symmetric-space formulations for the principal chiral fields, and for the self-dual Yang-Mills fields are given. Our formulation can easily be adapted to the corresponding supersymmetric fields.

Exact factorized S-matrix of the chiral field in two dimensions

The exact factorized S-matrix and the spectrum for the two-dimensional SU( N)-principal chiral field are presented.

Symplectic structure, Lagrangian, and involutiveness of first integrals of the principal chiral field equation

We deal with a form of the chiral equation, for which first integrals can be written explicitly. For these equations, we find a symplectic structure, the Lagrangian and first integrals in involution.

KAC-MOODY algebra for two dimensional principal chiral models

A Darboux transformation depending on single continuous parameter t is constructed for a principal chiral field. The transformation forms a nonlinear representation of the group for any fixed value of t. Part of the kernel in the Riemann- Hilbert transform is shown to be-related to the Darboux trans- formation with its generators forming a Kac-Moody algebra. Conserved currents associated with the Kac-Moody algebra of the linearized equations and the Nöether current for the group transformations with fixed value of t are obtained.

Classification of the reductions of the equations of principal chiral fields

Classification of the reductions of the equations of principal chiral fields

Algebraic aspects of two-dimensional chiral fields. II

Algebraic methods, in the broad sense of the word, of the theory of solitons (the theory of nonlinear differential equations related to the Korteweg-de Vries equation) are described for the example of relativistically invariant, two-dimensional, principal chiral fields.

Quantum and classical lattices for two-dimensional principal Chiral fields

Quantum and classical lattices for two-dimensional principal Chiral fields

Bäcklund transformations and local conservation laws for principal chiral fields

We construct a parametric Bäcklund transformation for principal chiral fields, which can then be used to derive local conservation laws.

On the integrability of classical spinor models in two-dimensional space-time

Well known classical spinor relativistic-invariant two-dimensional field theory models, including the Gross-Neveu, Vaks-Larkin-Nambu-Jona-Lasinio and some other models, are shown to be integrable by means of the inverse scattering problem method. These models are shown to be naturally connected with the principal chiral fields on the symplectic, unitary and orthogonal Lie groups. The respective technique for construction of the soliton-like solutions is developed.

Conservation laws and elements of scattering theory for principal chiral fields (d=1)

Conservation laws and elements of scattering theory for principal chiral fields (d=1)

Local conservation laws of principal chiral fields (d=1)

Local conservation laws of principal chiral fields (d=1)