Arthur Jaffe

Arthur Jaffe is one of the founders (with J. Glimm) of the subject called constructive quantum field theory, as opposed to axiomatic qft. This work led to the proof that several models of quantum field theory, when constructed carefully, obey the Wightman axioms; this holds in 2 and 3 space-time dimensions. So far, there is no proof that a Wightman theory with non-trivial scattering exists in four space-time dimensions. Glimm and Jaffe have also led the research into the construction of non-abelian gauge theories. Their book, "Quantum Physics", Springer, explains how they achieve their results. See here for comments on this programme.