A Selective Survey of Ideas, Tools and Results in Constructive Field Theory

In this talk we discuss some aspects of constructive field theory with an emphasis on analytical and probabilistic methods and results. In particular after an overview of some points in the history of constructive QFT we plan to discuss some early achievements in axiomatic QFT, some features of the theory of distributions and the basic structure of the Wightman reconstruction theorem. We also introduce the Osterwalder-Schrader axioms and overview the strategy for the construction of nontrivial measures describing path-integrals for interacting QFTs.
Depending on time constraints we might also discuss probabilistic tools (weak convergence of measures, the Bochner-Minlos theorem etc), Gaussian measures, UV regularity of simple QFTs and the construction of (infinite volume) Euclidean P(phi)_2 measures. The plan is to discuss some of these topics in some detail after the end of the official seminar.