Constructive quantum field theory
In mathematical physics, constructive quantum field theory is the field whose objective is to establish existence theorems for models of quantum field theory. Such theorems were proved in the 1960's and 1970's for quantum field theory models in two and three dimensional space-times in the papers by James Glimm, Arthur Jaffe, Irving Segal, Edward Nelson, and others. The main goal of constructive quantum field theory, an existence proof of non-trivial quantum field theory models in a four dimensional space-time, has not been reached. In the meantime, the theoretical physics community came to believe that the current state of the art quantum field theory models are merely effective, rather than fundamental, theories, whose mathematical status is of little practical relevance, and interest in constructive quantum field theory has waned.
- Summers, Stephen J.; A Perspective on Constructive Quantum Field Theory .