On the Existence of Kink-(Soliton-)States

TL;DR

This paper investigates the conditions under which kink-states, interpolating between different vacua, can be constructed in two-dimensional quantum field theories using algebraic quantum field theory, providing a general framework for such states.

Contribution

It establishes a general method for constructing kink-states between different vacua in a broad class of 2D quantum field theories within algebraic quantum field theory.

Findings

A natural construction method for kink-states in many models.

Applicable to vacua of P(φ)_2 models.

Supports structural understanding of soliton states.

Abstract

There are several two dimensional quantum field theory models which are equipped with different vacuum states. For example the Sine-Gordon- and the $\phi^4_2$-model. It is known that in these models there are also states, called soliton- or kink-states, which interpolate different vacua. We consider the following question: Which are the properties a pair of vacuum sates must have, such that an interpolating kink-state can be constructed? Since we are interested in structural aspects and not in specific details of a given model, we are going to discuss this question in the framework of algebraic quantum field theory which includes, for example, the $P(\phi)_2$-models. We have shown that for a large class of vacuum states, including the vacua of the $P(\phi)_2$-models, there is a natural way to construct an interpolating kink-state.