Boundary Effects in Integrable Field Theory on a Half Line

TL;DR

This paper investigates how boundary interactions in integrable field theories on a half line affect the classical and quantum properties, revealing that some integrable boundaries can significantly alter or destabilize the theories.

Contribution

It analyzes boundary effects in integrable field theories, identifying conditions for integrability and showing that some boundaries can cause instability or change the theory's character.

Findings

Certain boundary interactions preserve integrability at classical and quantum levels.

Some integrable boundaries lead to instability, making the theory ill-defined.

Boundary effects can drastically change the nature of the field theory.

Abstract

Abstarct: Boundary effects caused by the boundary interactions in various integrable field theories on a half line are discussed at the classical as well as the quantum level. Only the so-called ``integrable" boundary interactions are discussed. They are obtained by the requirement that certain combinations of the lower members of the infinite set of conserved quantities should be preserved. Contrary to the naive expectations, some ``integrable" boundary interactions can drastically change the character of the theory. In some cases, for example, the sinh-Gordon theory, the theory becomes ill-defined because of the instability introduced by ``integrable" boundary interactions for a certain range of the parameter.