On October 15, 2025, Sourav Chatterjiee gave the second of the Millenium prize lectures. I have started a page on this here where slides are included.
A bit of nostalgia
Some of my own course assistants or grad student colleagues worked on constructive quantum
field theory and not all graduated. Pierre-Alain Bovier or Felix finster are success examples. Already in 1990 the steam was a bit missing in Euclidean constructive quantum field theory. Konrad Osterwalder himself turned to more administration, later would become Rector at EThZ or
work at the UNU. Other folks in mathematical physics (like my PhD dad Oscar Lanford has started in QFT but changed to dynamical systems. If one looks at the
Student list of Arthur Wightman then many seem have have moved on to other topics.
Some comments
- The functional integrals make every mathematician nervous. I like the probabilistic approach where you have the Wiener measure as this is rigorous. The functional integrals written down formally just are too adventurous for mathematicians.
- As for the Maxwell equations, it really is much easier to write it relativistically. The Maxwell equations are dF=0, d*F=0 implying the wave equation L F = 0, where L=dd^*+d* d. Gauge transformation are
.
- The Yang-Mills existence problem is mathematically not defined in this talk.
- The mass gap problem is is not defined in the talk. What is the Markov process. What is the Hamiltonian? Is one free to make this up? One can make up quite general Hamiltonians with a Mass gap.
- Monte Carlo simulations of lattice gauge theories were fashion already many decades ago. I was fascinated by it and even wrote an article in this area.
- Balaban’s work that has been mentioned in the talk had been was fashion when I was a student. Here is one of the papers here at Harvard in 1987. I myself can not read this. It seems that many others have similar difficulties.
- My perception has not changed that this field of mathematical physics is too technical to be interesting. What was new to me from the talk that the problem has morphed to a problem in probability theory.
- The Wick rotation really does not seem to help much to gain insight into physics. It is a technical tool to make things converge. Analytic continuation can be a tricky business. Who knows what singularities lurk there. For me it can make perfect sense to use the analytic continuation of the Riemann zeta function to make sense of the determinant of the Laplacian of the circle. However, it is not trivial to prove that an analytic continuation is possible.
