6,355 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 the classification of quantum W-algebras
In this paper we consider the structure of general quantum W-algebras. We
introduce the notions of deformability, positive-definiteness, and reductivity
of a W-algebra. We show that one can associate a reductive finite Lie algebra
to each reductive W-algebra. The finite Lie algebra is also endowed with a
preferred subalgebra, which gives the conformal weights of the
W-algebra. We extend this to cover W-algebras containing both bosonic and
fermionic fields, and illustrate our ideas with the Poisson bracket algebras of
generalised Drinfeld-Sokolov Hamiltonian systems. We then discuss the
possibilities of classifying deformable W-algebras which fall outside this
class in the context of automorphisms of Lie algebras. In conclusion we list
the cases in which the W-algebra has no weight one fields, and further, those
in which it has only one weight two field.Comment: 28 page
Parafermionic Representation of the Affine Algebra at Fractional Level
The four fermionic currents of the affine superalgebra at
fractional level , u positive integer, are shown to be realised in
terms of a free scalar field, an doublet field and a primary field of
the parafermionic algebra .Comment: 5 pages, Latex 2
Multi-dimensional tunnelling and complex momentum
The problem of modeling tunneling phenomena in more than one dimension is examined. It is found that existing techniques are inadequate in a wide class of situations, due to their inability to deal with concurrent classical motion. The generalization of these methods to allow for complex momenta is shown, and improved techniques are demonstrated with a selection of illustrative examples. Possible applications are presented
Tunnelling from non-localised initial states
An approach for calculating tunneling amplitudes from a nonlocalized initial state is presented. Generalizing the matching conditions and equations of motion to allow for complex momentum permits a description of tunneling in the presence of so-called classical motion. Possible applications of the method are presented
Soliton-preserving boundary condition in affine Toda field theories
We give a new integrable boundary condition in affine Toda theory which is
soliton-preserving in the sense that a soliton hitting the boundary is
reflected as a soliton. All previously known integrable boundary conditions
forced a soliton to be converted into an antisoliton upon reflection. We prove
integrability of our boundary condition using a generalization of Sklyanin's
formalism.Comment: 9 page
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
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