Construction of Kink Sectors for Two-Dimensional Quantum Field Theory Models. An Algebraic Approach

TL;DR

This paper develops a method to construct kink states in two-dimensional quantum field theories, leveraging algebraic quantum field theory and the dynamics of specific models, aiming for broader applicability beyond free fields.

Contribution

It introduces a new construction scheme for kink states applicable to a wide class of models, bypassing the need for the split property in wedge algebras.

Findings

Constructed kink states using model dynamics.

Applicable to $P(\

Yukawa_2$ models and beyond.

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 in these models there are also 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 a large class of quantum field theory models, by making use of the properties of the dynamics of a $P(\phi)_2$ and Yukawa$_2$ models.