Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method

Journal Article · Thu Jun 01 04:00:00 EDT 1978 · Sov. Phys. - JETP (Engl. Transl.); (United States)

OSTI ID:6334118

Zakharov, V E; Mikhailov, A V

A method is proposed for deriving and classifying relativistically invariant integrable systems that are sufficiently general to encompass all presently known two-dimensional solvable models, and for the construction of a few new ones. The concept of ''gauge equivalence'' introduced in this paper allows one to clarify the relation between several different models of classical field theory, such as the n-field, the sine-Gordon equation, and the Thirring model. We study the model of the principal chiral field for the group SU (N). It is shown that at N=3 this model exhibits nontrivial interactions: decay, fusion and resonant scattering of solitons. New chiral models are proposed with fields taking values in homogeneous spaces of Lie groups and exhibiting a high degree of symmetry. We prove the integrability of these models when the homogeneous space is a Grassmann manifold.

• Research Organization: L. D. Landau Institute for Theoretical Physics, USSR Academy of Sciences
• OSTI ID: 6334118
• Journal Information: Sov. Phys. - JETP (Engl. Transl.); (United States), Journal Name: Sov. Phys. - JETP (Engl. Transl.); (United States) Vol. 47:6; ISSN SPHJA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHIRAL SYMMETRY
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
INTEGRALS
INVERSE SCATTERING PROBLEM
LIE GROUPS
QUASI PARTICLES
SINE-GORDON EQUATION
SOLITONS
SU GROUPS
SYMMETRY
SYMMETRY GROUPS
THIRRING MODEL
TWO-DIMENSIONAL CALCULATIONS