Fe b 20 05 Towards the construction of quantum field theories from a factorizing S - matrix ∗

An Existence Proof for Interacting Quantum Field Theories with a Factorizing S-Matrix

Within the context of quantum field theories on two-dimensional Minkowski space with a factorizing S-matrix, a new construction scheme for relativistic model theories is carried out. We show that for a large class of such S-matrices, there exists an associated local quantum field theory in the sense of Haag and Kastler. The crucial step in this approach consists in proving the existence of obse...

On the Construction of Quantum Field Theories with Factorizing S-Matrices

Construction of Quantum Field Theories with Factorizing S-Matrices

A new approach to the construction of interacting quantum field theories on two-dimensional Minkowski space is discussed. In this program, models are obtained from a prescribed factorizing S-matrix in two steps. At first, quantum fields which are localized in infinitely extended, wedge-shaped regions of Minkowski space are constructed explicitly. In the second step, local observables are analyz...

X iv : m at h - ph / 0 40 50 62 v 1 2 6 M ay 2 00 4 On the Existence of Local Observables in Theories With a Factorizing S – Matrix

A recently proposed criterion for the existence of local quantum fields with a prescribed factorizing scattering matrix is verified in a non-trivial model, thereby establishing a new constructive approach to quantum field theory in a particular example. The existence proof is accomplished by analyzing nuclearity properties of certain specific subsets of Fermionic Fock spaces.

Algebraic constructive quantum field theory: Integrable models and deformation techniques

Several related operator-algebraic constructions for quantum field theory models on Minkowski spacetime are reviewed. The common theme of these constructions is that of a Borchers triple, capturing the structure of observables localized in a Rindler wedge. After reviewing the abstract setting, we discuss in this framework i) the construction of free field theories from standard pairs, ii) the i...