On the Existence of Kink-(Soliton-)States

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.Comment: 23pp, latex2e, replaced versio

On the Algebraic Theory of Soliton and Antisoliton Sectors

We consider the properties of massive one particle states on a translation covariant Haag-Kastler net in Minkowski space. In two dimensional theories, these states can be interpreted as soliton states and we are interested in the existence of antisolitons. It is shown that for each soliton state there are three different possibilities for the construction of an antisoliton sector which are equivalent if the (statistical) dimension of the corresponding soliton sector is finite.Comment: 33pp, latex2e. to appear in Rev. Math. Phy

From euclidean field theory to quantum field theory

In order to construct examples for interacting quantum field theory models, the methods of euclidean field theory turned out to be powerful tools since they make use of the techniques of classical statistical mechanics. Starting from an appropriate set of euclidean n-point functions (Schwinger distributions), a Wightman theory can be reconstructed by an application of the famous Osterwalder-Schrader reconstruction theorem. This procedure (Wick rotation), which relates classical statistical mechanics and quantum field theory, is, however, somewhat subtle. It relies on the analytic properties of the euclidean n-point functions. We shall present here a C*-algebraic version of the Osterwalder-Scharader reconstruction theorem. We shall see that, via our reconstruction scheme, a Haag-Kastler net of bounded operators can directly be reconstructed. Our considerations also include objects, like Wilson loop variables, which are not point-like localized objects like distributions. This point of view may also be helpful for constructing gauge theories.Comment: 35 page