QM Research Seminar: Generalized inductive systems, convergence of dynamics, and renormalization

Speaker: Alexander Stottmeister (University of Hannover)


Abstract:

I will discuss a generalized notion of inductive systems of Banach spaces, coined soft inductive systems, that can serve as a flexible tool to describe the limits of physical theories, e.g., in the context of the thermodynamic limit and phase transitions or renormalization of quantum field theories.
General criteria for the convergence of dynamics can be obtained in this setting, which I will illustrate using the example of renormalization of free fermion theories on a one-dimensional spatial lattice. Specifically, this example can be used to prove the conformal invariance of various correlation functions of the classical Ising model using operator algebraic methods.

This talk is based on work with L. van Luijk, T.J. Osborne, and R.F. Werner.