Renormalization, dynamics, and spontaneous symmetry breaking

New York University, New York NY

Investigators

Abstract

The renormalization group method is a cornerstone of modern theoretical physics, explaining a vast range of central phenomena from areas spanning from elementary particle to solid state physics and beyond. The main idea is the analysis of an effective description of a theory at different length scales, leading to a dynamics as the scale varies---the renormalization group dynamics. The mathematics of the renormalization group however is only well understood in very few cases. One of the main goals of this project is to develop mathematical methods and examples of the renormalization group in different contexts. Graduate students wills be mentored as part of the project; the awardee will present courses on relevant material and make their lecture notes available, and also participate in outreach programs for K12 students. The main focus of this proposal is on the use of the renormalization group method in two contexts, the small and large scale properties of stochastic dynamics of statistical field theories, and the mathematics of spontaneously broken continuous symmetries, in particular in the example of the OSp(1|2) non-linear sigma model. In a complementary direction, some examples of integrable quantum field theories will be explored as well. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.