I'm wondering about current efforts to provide mathematical
foundations and more solid definition for quantum field theories. I
am aware of such efforts in the context of the simpler topological
or conformal field theories, and of older approaches such as
algebraic QFT, and the classic works of Wightman, Streater, etc.
etc . I am more interested in more current approaches, in
particular such approaches that incorporate the modern
understanding of the subject, based on the renormalization group. I
know such...