Informational and algebraic renormalization group

The renormalization group (RG) is one of the central ideas in theoretical physics, lying at the heart of how we describe low-energy effective theories. In this talk, I will show how Wilsonian RG can be reformulated as a quantum channel and as an algebraic operation. This allows us to extend RG beyond quantum field theory to quantum many-body systems and even systems with finitely many degrees of freedom. I will also discuss how the irreversibility of coarse graining can be understood from a resource-theoretic perspective, which leads to a systematic way of constructing RG monotones. This talk is based on joint work with T. Nagasawa (Kanazawa University), which will appear on arXiv on Monday, September 28.