Marcel Riesz’s Lecture Notes on Clifford Algebra

Abstract

[During a walk in Boston, Mass in the fall of 1955 Professor Marcel Riesz asked me what I was doing at the Research Laboratory of Electronics, MIT. Cambridge, Mass. I answered that for the time being I was cascading lossv two port networks by means of the Schilling figure in the three-dimensional (3D) Cayley-Klein model of hyperbolic space. Riesz looked very surprised and asked why I used these beautiful mathematical tools and I said that I wanted to study transformations of noise in network theory and partially polarized waves in electromagnetic theory and that I had to use 3D and 4D spaces, for example, the 3D and 4D Minkowski models of Lorentz space. Riesz said that the natural tool to use is the Clifford algebra. He promised to give me private lectures on Clifford algebra. Thus, lectures were given in Stockholm, Sweden (July-August 1956), at the University of Maryland, College Park, Maryland (November 1958), at my home at Lexington, Mass (Febr 1959) in connection with an invited talk at the U.S. Air Force Bedford, Mass, and finally at the Indiana University, Bloomington, Indiana (April 1959). Riesz dictated while he walked around in the room. He never looked at any paper. Only the Indiana notes were dictated in English, the others in Swedish. Riesz worked a lot on generalizing the Schilling figure and the Pascal theorem to the 4D Lorentz space. On February 8, 1959 he told me that his Notes on Clifford Algebra would have six chapters. He had started on the fifth chapter on December 1, 1958. It would contain special features of 4D space-time, the Schilling figure, Pascal’s theorem, etc. The sixth chapter would deal with spinors.]