3,754 research outputs found
Classical backgrounds and scattering for affine Toda theory on a half-line
We find classical solutions to the simply-laced affine Toda equations which
satisfy integrable boundary conditions using solitons which are analytically
continued from imaginary coupling theories. Both static `vacuum' configurations
and the time-dependent perturbations about them which correspond to classical
vacua and particle scattering solutions respectively are considered. A large
class of classical scattering matrices are calculated and found to satisfy the
reflection bootstrap equation.Comment: Latex document, 28 pages, 3 figures include
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.Comment: 6 pages, to appear in Proceedings of the XVth International
Colloquium on Integrable Systems and Quantum Symmetries, Prague, June 200
Semiclassical analysis of defect sine-Gordon theory
The classical sine-Gordon model is a two-dimensional integrable field theory,
with particle like solutions the so-called solitons. Using its integrability
one can define its quantum version without the process of canonical
quantization. This bootstrap method uses the fundamental propterties of the
model and its quantum features in order to restrict the structure of the
scattering matrix as far as possible. The classical model can be extended with
integrable discontinuities, purely transmitting jump-defects. Then the quantum
version of the extended model can be determined via the bootstrap method again.
But the outcoming quantum theory contains the so-called CDD uncertainity. The
aim of this article is to carry throw the semiclassical approximation in both
the classical and the quantum side of the defect sine-Gordon theory. The CDD
ambiguity can be restricted by comparing the two results. The relation between
the classical and quantum parameters as well as the resoncances appeared in the
spectrum are other objectives
On a systematic approach to defects in classical integrable field theories
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 Backlund 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 -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.Comment: 27 pages, no figures. Final version accepted for publication.
References added and section 5 amende
Integrable Field Theories with Defects
The structure of integrable field theories in the presence of defects is
discussed in terms of boundary functions under the Lagrangian formalism.
Explicit examples of bosonic and fermionic theories are considered. In
particular, the boundary functions for the super sinh-Gordon model is
constructed and shown to generate the Backlund transformations for its soliton
solutions.Comment: talk presented at the XVth International Colloquium on Integrable
Systems and Quantum Symmetries, to appear in Czechoslovak Journal of Physics
(2006
From Defects to Boundaries
In this paper we describe how relativistic field theories containing defects
are equivalent to a class of boundary field theories. As a consequence
previously derived results for boundaries can be directly applied to defects,
these results include reduction formulas, the Coleman-Thun mechanism and
Cutcosky rules. For integrable theories the defect crossing unitarity equation
can be derived and defect operator found. For a generic purely transmitting
impurity we use the boundary bootstrap method to obtain solutions of the defect
Yang-Baxter equation. The groundstate energy on the strip with defects is also
calculated.Comment: 14 pages, 10 figures. V2 Removed comparison to RT algebras and added
paragraph on the usefulness of transmitting defects in the study of boundary
systems. References added. V3 Extended to include application to defect TB
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