About the topic:
In both statistical and quantum physics, one is interested in the construction of certain measures on spaces of elds. Famously, a naive approach to these in nite dimensional measures is plagued by divergences, and this has gradually come to be physically understood in terms of a multiscale analysis known as renormalization theory. The entailing conceptual understanding, however, has not yet been paralleled by a mathematical theory which is able to provide us with the relevant measures for the description of the world we inhabit (rigorous models have only been constructed in spatial dimensions 1 and 2). In this talk, I will introduce renormalization theory using a new approach, based on incorporating the fact that the space-time continuum is an idealization by using a projective limit description of the space of functions on a manifold. This leads immediately to the concepts of continuous product measures and Lévy white noise elds. It also allows for a clean and simple generalization of the Wick calculus in stochastic analysis and quantum eld theory, which works seamlessly for non-gaussian measures on spaces of elds over arbitrary manifolds. Finally, I will demonstrate how this approach promises to solve the problems mentioned above, by constructing several reasonable candidates for non-trivial scalar eld theories in arbitrary space-time dimension.
About the speaker:
Rodrigo Vargas Le-Bert is a postdoctoral researcher at Universita di Camerino, Italy. His work is motivated by the desire to better understand our fundamental models of nature. He has made contributions in the areas of repeated interaction quantum systems, integrability of involutive algebra representations, and the geometry of non-integrable Lie algebra representations. More recently, he has turned to constructive eld theory, where he is developing a projective approach to functional integration with applications in stochastic analysis and quantum eld theory. After his studies in Santiago de Chile, New York and Paris, Rodrigo obtained his PhD in Grenoble. Later, he worked as CONICYT postdoctoral fellow at Universidad de Talca and associate professor at Universidad Austral, both in Chile.