I only learned recently thought the “not even wrong” blog that Konrad Osterwalder passed away last December. He had been department head at ETHZ from 1986-1990 which overlapped quite a bit with my graduate student time. He then became rector of ETHZ and became later an important figure in the united nations but he had some graduate students that were also assistants but I could only admire and not appreciate the difficulty of the problems they were working on. I never took a course taught by Osterwalder but I took quantum mechanics from his advisor Klaus Hepp and mechanics from Juerg Froehlich, an other student of Hepp. Res Jost (whom I never met) had been an other advisor of Osterwalder and I took electromagnetism from Jost’s student Walter Hunziker, a symplectic geometry course from his student Eduard Zehnder (who also passed away recently) and a postgraduate course about dynamical zeta function by David Ruelle.
Already then, while I was in graduate school, it appeared (maybe it was less obvious yet) that axiomatic quantum field theory was more difficult than anticipated. This mathematical axiomatic approach was spear headed by Arthur Wightman (my academic grand father …) but my academic father Oscar Lanford had moved on from the subject to greener pastures like dynamical systems theory. Also other students of Wightman like Jerold Marsden or Barry Simon had branched off to other topics in applied mathematics or mathematical physics.
Osterwalder might not know this but he was quite important to me like becoming a course assistant and later graduate student. Quite early on as a graduate student, I was asked by Osterwalder to look into chapter 12 of the book of Cycon-Froese-Kirsch and Simon to assist in a seminar on Patodi’s proof of the Gauss-Bonnet-Chern theorem. I spent a week alone on the alp “Salmenfee” in the Swiss mountains during a summer break, working through that chapter. The seminar eventually did not take place; the exposure to that book however turned out to be life changing for me as the book contained a nice concise introduction into modern Riemannian geometry. Having seen in college only a basic undergraduate differential geometry course, by Max Jeger, focusing on curves and surfaces, this widened my horizon. The book also contains a chapter on almost periodic Schroedinger operators, a topic that is closely related to ergodic theory, and a relatively fresh area of mathematics. The topic had been popularized especially in the form of the Hofstadter butterfly which I had read in high school. The concept of Lyapunov exponents of transfer matrices touches upon chaos theory, something which appeared in my senior thesis at ETHZ. So, I’m sure that without that “nudge” to look into that book, my thesis would have have taken different turns.
An other encounter happened at the SOLA Staffette, a traditional run over more than 100 km where a team of 14 run 14 sections. It is the largest university sports event in Switzerland and I just saw that it still takes place in a similar manner today. I remember having run somewhere near Zumikon or Zollikon and that I passed the stick to Konrad Osterwalder who was also in the “Mathematicians Team”. This must have been around 1990. I’m not sure whether the route was the same then as it is now, but what I see on this page looks about right. Osterwader was then close to 50 but top fit and ripped.
In mathematics, Osterwalder is most obviously linked with the Osterwalder-Schrader axioms from 1972, while he as a postdoc at Harvard. It is an axiom system for Wightman distributions. The choice of distributions is a kind of interesting philosophically and is a case where the difference between “geometries” and “fields” is huge. Distributions are the dual of smooth functions. There is an other intereresting point in that Euclidean quantum field theory can be analytically continued into a Lorentzian case. The point of the approach was to work with Euclidean Schwinger functions and then show that this can be carried over to a Minkowski quantum field theory. It appears however that for realistic 4 dimensional field theories, one just has no interesting example. This triviality conundrum is what I understand to be part of the mass gap problem which Sudan talked about last December. I don’t know much about this part of mathematical physics but it seems that the problem is just too difficult and that different approaches are needed.
I only very briefly met Osterwalder here at Harvard, once when he had been discussing with Arthur Jaffe in the LISE coffee shop and Jaffe told that they plan to write a new paper. That was maybe 10 years ago.
