Kink States in $P(\phi)_2$-Models (An Algebraic Approach)

TL;DR

This paper develops a method to construct kink states in two-dimensional $P( ext{phi})_2$ quantum field models, relying on algebraic quantum field theory and properties of the model's dynamics, aiming to extend known results beyond free fields.

Contribution

It introduces a new construction scheme for kink states in $P( ext{phi})_2$-models that does not depend on the split property of wedge algebras.

Findings

Constructed kink states directly for $P( ext{phi})_2$-models.

Utilized properties of the model's dynamics for the construction.

Provided a framework applicable to models with multiple vacua.

Abstract

Several two-dimensional quantum field theory models have more than one vacuum state. Familiar examples are the Sine-Gordon and the $\phi^4_2$-model. It is known that these models possess states, called kink states, which interpolate different vacua. A general construction scheme for kink states in the framework of algebraic quantum field theory is developed in a previous paper. However, for the application of this method, the crucial condition is the split property for wedge algebras in the vacuum representations of the considered models. It is believed that the vacuum representations of $P(\phi)_2$-models fulfill this condition, but a rigorous proof is only known for the massive free scalar field. Therefore, we investigate in a construction of kink states which can directly be applied to $P(\phi)_2$-model, by making use of the properties of the dynamic of a $P(\phi)_2$-model.