Axiomatic quantum field theory (e.g. the wightman formalism and constructive quantum field theory) is an important subject. When I look into textbooks and papers, I mostly find that the basic constructions involve functional analysis and operator algebra. Now, modern developments in the field of quantum field theory involve subjects such as algebraic geometry, topology, and knots. Mostly modern developments deal with supersymmetric quantum field theory.

My question is: What is the status of current research on the mathematical foundations of the dynamics of "non topological" quantum field theory? Are the older approaches to the subjects, such as the ones in Glimm and Jaffe's and Wightman's books, obsolete?