Tribute to Henri Epstein by Arthur M. Jaffe

Henri Epstein was a deep thinker who made important progress both in quantum field theory and in dynamical systems. He was also a dear friend.

We first met over sixty years ago, during the 1963—64 academic year at IHES, marking its beginning in Bures-sur-Yvette. During that time the first part of the scientific building was only under construction, and researchers had to find other places to work. But the tearoom in the main building (then with most of the professors’ offices) provided a wonderful place to interact. My teacher, Arthur Wightman, helped organize a year-long workshop on mathematical foundations of quantum field theory, so it was wonderful to be included while still a student. Jurko Glaser was there as well, and Henri was engrossed in their program with Jacques Bros to understand the analyticity properties in quantum field theory that were a consequence of the Wightman axioms.

During that period that the three of us wrote a small paper showing that the energy density in any Wightman quantum field theory could not be positive. It is remarkable that one still finds many citations of this result. Later Henri became interested in the Feigenbaum fixed point, and he gave an ingenious convergence proof.

Henri and I got to know each other much better during the IHES year by attending weekly (along with Jean Lascoux) the course of Laurent Schwartz, held at the Institut Henri Poincaré. We often did something together after the class, and Henri became my expert advisor on where to dine in Paris. Some years later I discovered that Henri (as well as Nicolas Sourlas and Jean Iliopolous) were wonderful cooks. During subsequent visits to Paris we enjoyed several meals that they prepared, rivaling the best addresses they could recommend.

In 1964—65 Henri came to Princeton as a post-doctoral fellow, where his insights were highly appreciated, despite his enormous modesty. We interacted a great deal not only with Wightman, but also with Klaus Hepp, Gian-Fausto Dell Antonio, and Hans Borchers. I took a photo (above) of Henri with this group while boarding a plane on the way to a conference in Cambridge, Massachusetts organized by I. Segal. The second photo (below) is in the yard of the home of Edward Nelson one Princeton afternoon, also with Arthur Wightman.

A few years later I gave a colloquium at CERN; at the time Henri was a member of the theory division. He suggested that we meet the next day for lunch. Henri picked Shelly Glashow and me up in his car that morning, and without explanation, off we went to Paul Bocuse in Lyon. Henri had reserved a table; it was a beautiful afternoon on the terrace! Through this extraordinary outing, Henri introduced me for the first time to “3-star” French cuisine.

I saw Henri and his sister last during the 2022 Ising meeting at IHES, spending an afternoon at their home on the rue de Vaugirard. Along with his other acquaintances, we will miss Henri’s humor, his generosity, his friendship, as well as his great insights into mathematical physics.

Arthur Jaffe
Cambridge, Massachusetts
September 10, 2024