Factorized Scattering in the Presence of Reflecting Boundaries

TL;DR

This paper develops a set of consistency equations for scattering matrices with reflecting boundaries, deriving explicit formulas for the reflection matrix in affine Toda theories.

Contribution

It introduces a bootstrap-like equation involving the W-matrix for particles reflecting off boundaries, providing explicit solutions in affine Toda models.

Findings

Derived a bootstrap equation for the W-matrix

Provided explicit formulas for W in affine Toda theories

Established consistency conditions for boundary scattering matrices

Abstract

We formulate a general set of consistency requirements, which are expected to be satisfied by the scattering matrices in the presence of reflecting boundaries. In particular we derive an equivalent to the boostrap equation involving the W-matrix, which encodes the reflection of a particle off a wall. This set of equations is sufficient to derive explicit formulas for $W$, which we illustrate in the case of some particular affine Toda field theories.