Entanglement and renormalization

Abstract

An important milestone in our understanding of QFTs was Wilson’s idea of the renormalization group [200, 201]. The idea that physics can be organized into energy scales and that the high-energy modes are irrelevant, and can be integrated out when describing low energy dynamics, is central to our understanding of effective field theories. While the microscopic dynamics are prescribed in terms of some fundamental degrees of freedom, if our interest is in computing observables that probe the quantum dynamics at macrophysical scales, we can coarse-grain the system and work with just the relevant modes at the scales of interest. Clearly, this procedure involves some loss of information owing to the coarse-graining—a natural question is how does one capture a useful measure of the number of degrees of freedom at each length scale?