3.30 pm, Seminar Hall CMI Silver Jubilee Lecture It is a Rough World In There: Regularity of Quantum Fields S.G. Rajeev University of Rochester, NY, U.S.A. 050815 Abstract Quantum Field Theory is the description of nature at the shortest distances we understand. Using wellestablished mathematical methods, we can investigate the regularity or roughness of quantum fields. It turns out that (after averaging over a small ball) free fields are Lipshitz functions with respect to a metric. But this metric is not Euclidean or Riemannian; with respect to any such metric quantum fields are hopelessly rough (not even continuous). Our result generalizes Levy's continuity modulus for Brownian motion . This suggests that at short distances spacetime is a (nonRiemannain) metricmeasure space; enough structure to define a laplacian and hence the action of a scalar quantum field. Asymptotically free quantum fields have a similar behavior at short distances to free fields. I will give some preliminary results for interacting quantum fields with a Landau singularity.
