On a systematic approach to defects in classical integrable field theories
نویسنده
چکیده
We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of modified integrals of motion. The contribution of the defect to all orders is explicitely identified in terms of a defect matrix. The underlying geometric picture is that those defects correspond to Bäcklund transformations localized at a given point. A classification of defect matrices as well as the corresponding defect conditions is performed. The method is applied to a collection of well-known integrable models and previous results are recovered (and extended) directly as special cases. Finally, a brief discussion of the classical r-matrix approach in this context shows the relation to inhomogeneous lattice models and the need to resort to lattice regularizations of integrable field theories with defects. PACS numbers: 02.30.Ik, 02.30.Jr, 02.30.Zz, 11.10.Kk, 11.10.Lm E-mail: [email protected]
منابع مشابه
Purely Transmitting Integrable Defects * )
Some aspects of integrable field theories possessing purely transmitting defects are described. The main example is the sine-Gordon model and several striking features of a classical field theory containing one or more defects are pointed out. Similar features appearing in the associated quantum field theory are also reviewed briefly. 1 Classical picture The context of this topic is two-dimensi...
متن کاملAspects of Purely Transmitting Defects in Integrable Field Theories
Some classical and quantum aspects of integrable defects are reviewed with particular emphasis on the behaviour of solitons in the sine-Gordon model.
متن کاملFolding defect affine Toda field theories
A folding process is applied to fused a(1) r defects to construct defects for the non-simply laced affine Toda field theories of c(1) n , d (2) n and a (2) 2n at the classical level. Support for the hypothesis that these defects are integrable in the folded theories is given by the demonstration that energy and momentum are conserved. Further support is provided by the observation that transmit...
متن کاملDefects in affine Toda field theories
In this talk some classical and quantum aspects concerning a special kind of integrable defect called a jump-defect will be reviewed. In particular, recent results obtained in an attempt to incorporate this defect in the affine Toda field theories, in addition to the sine-Gordon model, will be presented. 1 E-mail: [email protected]
متن کاملSelected Topics in Classical Integrability
Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete and continuum classical integrable models is introduced. Using this framework the associated classical integrals of motion and the corresponding Lax pair ar...
متن کامل