Boundary states in integrable quantum field theory

Abstract

The purpose of this talk is to sketch some recent progress which has been made in calculating non-perturbatively the reflection factors for the sinh-Gordon model restricted to a half-line by integrable boundary conditions. The essential idea is to calculate the energy spectrum of boundary breathers in two independent ways; firstly by using the boundary bootstrap and secondly by quantizing the classical solutions corresponding to boundary breathers. Comparing these two calculations provides a way to determine the dependence of the reflection factors on the parameters introduced into the Lagrangian by the boundary conditions. The basic idea is illustrated using a massive free scalar field with a linear boundary condition confining it to a half-line.

From Hamiltonian to zero curvature formulation for classical integrable boundary conditions

“…This gap in the theory has been described under various forms in the literature, with no satisfactory answer to the best of our knowledge. For instance, in [19], the author reviews some results [20,21] which took the view of modifying in an ad hoc fashion the bulk Lax pair in order to accommodate integrable boundary conditions. The dynamical generalisation of (1) appears as a consistency condition in this approach.…”

Second Order Quantum Corrections to the Classical Reflection Factor of the Sinh–gordon Model

“…[18]). Comparing these two calculations provides a relationship between the boundary parameters, the bulk coupling constant and the parameters in Ghoshal's formula.…”