# Coupling integrable field theories to mechanical systems at the boundary

@article{Baseilhac2001CouplingIF, title={Coupling integrable field theories to mechanical systems at the boundary}, author={Pascal Baseilhac and Gustav W. Delius}, journal={Journal of Physics A}, year={2001}, volume={34}, pages={8259-8270} }

We present an integrable Hamiltonian which describes the sinh-Gordon model on the half line coupled to a non-linear oscillator at the boundary. We explain how we apply Sklyanin's formalism to a dynamical reflection matrix to obtain this model. This method can be applied to couple other integrable field theories to dynamical systems at the boundary. We also show how to find the dynamical solution of the quantum reflection equation corresponding to our particular example.

## 25 Citations

### Coupling The Sine-Gordon Field Theory to a Mechanical System at the Boundary

- Mathematics
- 2002

We describe an integrable system consisting of the sine-Gordon field, restricted to the half line, and coupled to a non-linear oscillator at the boundary. By extension of the coupling constant to…

### Common structures of quantum field theories and lattice systems through boundary symmetry

- Mathematics
- 2011

The sine-Gordon model and affine Toda field theories on the half-line, on the one hand, the XXZ spin chain with nondiagoual boundary terms, and interacting many-body lattice systems with a flow, on…

### Integrability of the boundary sine-Gordon model

- Physics
- 2005

We construct a boundary Lagrangian for the supersymmetric sine-Gordon model which preserves (B-type) supersymmetry and integrability to all orders in the bulk coupling constant g. The supersymmetry…

### From Hamiltonian to zero curvature formulation for classical integrable boundary conditions

- Mathematics, PhysicsJournal of Physics A: Mathematical and Theoretical
- 2018

We reconcile the Hamiltonian formalism and the zero curvature representation in the approach to integrable boundary conditions for a classical integrable system in 1 + 1 space-time dimensions. We…

### N = 2 boundary supersymmetry in integrable models and perturbed boundary conformal field theory

- Physics
- 2003

### Infinite dimension reflection matrices in the sine-Gordon model with a boundary

- MathematicsJournal of High Energy Physics
- 2012

Using the sine-Gordon model as the prime example an alternative approach to integrable boundary conditions for a theory restricted to a half-line is proposed. The main idea is to explore the…

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