CMI Silver Jubilee Lecture
S.G. Rajeev, University of Rochester, USA
It is a Rough World In There: Regularity of Quantum Fields
Wednesday, August 5, 2015
Quantum Field Theory is the description of nature at the shortest distances we understand. Using well-established 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 space-time is a (non-Riemannain) metric-measure 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.