On the Construction of Quantum Field Theories with Factorizing S-MatricesMay 5th, 2006
The subject of this thesis is a novel construction method for interacting relativistic quantum field theories on two-dimensional Minkowski space. Employing the algebraic framework of quantum field theory, it is shown under which conditions an algebra of observables localized in a wedge-shaped region of spacetime can be used to construct model theories. A crucial input in this context is the modular nuclearity condition for wedge algebras, which implies the existence of local observables.
As an application of the new method, a rigorous construction of a large family of models with factorizing S-matrices is obtained. In an inverse scattering approach, a given factorizing scattering operator is used to define certain wedge-localized Wightman fields associated to it. The construction of these fields is due to Schroer and uses ideas of the form factor program (Zamolodchikov’s algebra). With the help of these fields, a wedge algebra can be defined, which determines the local observable content of a well-defined quantum field theory. In this approach, the modular nuclearity condition translates to certain analyticity and boundedness conditions on the formfactors of wedge-local observables. These conditions are shown to hold for a large class of underlying S-matrices, including the scattering operators of the Sinh-Gordon model and the scaling Ising model as special examples.
The so constructed models are investigated with respect to their scattering properties. They are shown to solve the inverse scattering problem for the underlying S-matrices, and a proof of asymptotic completeness for these models is given.
