# Classically integrable boundary conditions for affine Toda field theories

@article{Bowcock1995ClassicallyIB, title={Classically integrable boundary conditions for affine Toda field theories}, author={Peter Bowcock and Edward Corrigan and P. E. Dorey and R. H. Rietdijk}, journal={Nuclear Physics}, year={1995}, volume={445}, pages={469-500} }

Abstract Boundary conditions compatible with classical integrability are studied both directly, using an approach based on the explicit construction of conserved quantities, and indirectly by first developing a generalisation of the Lax pair idea. The latter approach is closer to the spirit of earlier work by Sklyanin and yields a complete set of conjectures for permissible boundary conditions for any affine Toda field theory.

#### 125 Citations

Background field boundary conditions for affine Toda field theories

- Physics
- 1995

Classical integrability is investigated for affine Toda field theories in the presence of a constant background tensor field. This leads to a further set of discrete possibilities for integrable… Expand

Classically integrable field theories with defects

- Physics
- 2003

Some ideas and remarks are presented concerning a possible Lagrangian approach to the study of internal boundary conditions relating integrable fields at the junction of two domains. The main example… Expand

Soliton-preserving boundary condition in affine Toda field theories

- Physics, Mathematics
- 1998

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… Expand

Integrable boundary conditions and modified Lax equations

- Physics, Mathematics
- 2008

Abstract We consider integrable boundary conditions for both discrete and continuum classical integrable models. Local integrals of motion generated by the corresponding “transfer” matrices give rise… Expand

Jumps and twists in affine Toda field theories

- Physics, Mathematics
- 2015

Abstract The concept of point-like “jump” defects is investigated in the context of affine Toda field theories. The Hamiltonian formulation is employed for the analysis of the problem. The issue is… Expand

Quantum integrability in two-dimensional systems with boundary

- Physics
- 1995

Abstract In this letter we consider affine Toda systems defined on the half-plane and study the issue of quantum integrability, i.e. the construction of higher-spin conserved currents in the presence… Expand

Classical backgrounds and scattering for affine Toda theory on a half-line

- Physics
- 1998

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.… Expand

Aspects of Classical Backgrounds and scattering for affine Toda theory on a half-line

- Physics
- 1999

In this paper we study various aspects of classical solutions to the affine Toda equations on a half-line with integrable boundary conditions. We begin by finding conditions that the theory has a… Expand

Classical and quantum integrable systems with boundaries

- Mathematics, Physics
- 1999

We study two-dimensional classically integrable field theory with independent boundary conditions at each end, and obtain three possible generating functions for integrals of motion when this model… Expand

Expectation Values of Boundary Fields in Integrable Boundary Toda Theories

- Physics
- 2001

Integrable boundary Toda theories are considered. We derive boundary reflection amplitudes and boundary two-point functions in the non-affine and one-point functions in affine Toda theories. The… Expand

#### References

SHOWING 1-10 OF 43 REFERENCES

Affine Toda field theory on a half-line

- Physics
- 1994

Abstract The question of the integrability of real-coupling affine toda field theory on a half-line is addressed. It is found, by examining low-spin conserved charges, that the boundary conditions… Expand

A remark on the coupling dependence in affine Toda field theories

- Physics
- 1993

Abstract The affine Toda field theories based on the non-simply-laced Lie algebras are discussed. By rewriting the S -matrix formulae found by Delius et al., a universal form for the… Expand

Integrable boundary conditions for classical sine-Gordon theory

- Mathematics, Physics
- 1995

The possible boundary conditions consistent with the integrability of the classical sine-Gordon equation are studied. A boundary value problem on the half-line x<or=0 with local boundary condition at… Expand

Affine Toda Field Theory in the Presence of Reflecting Boundaries

- Physics
- 1994

We show that the “boundary crossing-unitarity equation” recently proposed by Ghoshal and Zamolodchikov is a consequence of the boundary bootstrap equation for the S-matrix and the wall-bootstrap… Expand

Boundary conditions for integrable quantum systems

- Mathematics
- 1988

A new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering (R-matrix) method. The method proposed allows the author to treat open… Expand

Boundary conditions for integrable equations

- Mathematics
- 1997

The problem of constructing boundary conditions for nonlinear equations compatible with higher symmetries is considered. In particular, this problem is discussed for the sine - Gordon, Jiber -… Expand

AFFINE TODA FIELD-THEORY AND EXACT S-MATRICES

- Physics
- 1990

Abstract The masses and three-point couplings for all affine Toda theories are calculated. The exact factorisable S-matrices are conjectured on the basis of the classical masses and couplings and… Expand

Aspects of Affine Toda Field Theory on a Half Line

- Physics, Mathematics
- 1994

The question of the integrability of reaJ.coupling affine Toda field theory on a half line is discussed. It is shown, by examining low-spin conserved charges, that the boundary conditions preserving… Expand

The Toda lattice field theory hierarchies and zero-curvature conditions in Kac-Moody algebras

- Physics
- 1986

Abstract The two-dimensional Toda lattice field theories possess an infinite number of local conserved quantities in involution. These can be used as hamiltonians to define a consistent simultaneous… Expand

MULTIPLE POLES AND OTHER FEATURES OF AFFINE TODA FIELD-THEORY

- Physics
- 1991

Some perturbative features of affine Toda field theory are explored, in particular the mechanisms responsible for he first-, second- and third-order poles in the conjectured exact factorisable… Expand