George Mackey and His Work on Representation Theory and Foundations of Physics

This article is a retrospective view of the work of George Mackey and its impact on the mathematics of his time and ours. The principal themes of his work–systems of imprimitivity, induced representations, projective representations, Borel cohomology, metaplectic representations, and so on, are examined and shown to have been central in the development of the theory of unitary representations of arbitrary separable locally compact groups. Also examined are his contributions to the foundations of quantum mechanics, in particular the circle of ideas that led to the famous Mackey-Gleason theorem and a significant sharpening of von Neumann’s theorem on the impossibility of obtaining the results of quantum mechanics by a mechanism of hidden variables.