Deformations of Quantum Field Theories

The project aims at the construction and study of new models of relativistic quantum field theory employing a recently discovered method of deformations of operator algebras. Relativistic quantum field theory is the basis of modern high energy physics and has been spectacularly successful in that area. Mathematically rigorous constructions of interacting models going beyond perturbation theory or other approximation methods, are, however so far only known in space-time dimensions lower than four. An extension of the known arsenal of methods is an important challenge to mathematical physics and the main topic of the project.

Relativistic quantum field theory is the basis of modern high energy physics and has been spectacularly successful in that area. So far, however, only few mathematically rigorous constructions of models with interactions, that go beyond perturbation theory and other approximation methods, are known. The extension of the arsenal of methods has been an important challenge to Mathematical Physics since decades. In the project several new methods were developed and analysed, using techniques from the theory of operator algebras. Furthermore a number of new, concrete models, that cast light on various aspects of quantum field theory were found and studied.