The nonperturbative functional renormalization group and its applications

The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties systems on one hand other search for viable ultraviolet completions fundamental physics. It provides us with natural framework study theoretical models where degrees freedom are correlated over long distances that may exhibit very distinct behavior different energy scales. nonperturbative functional renormalization-group (FRG) approach is modern implementation Wilson’s RG, which allows set up approximation schemes go beyond standard perturbative RG approaches. FRG based exact flow equation coarse-grained effective action (or Gibbs free language statistical mechanics). We review main commonly used solve this discuss applications equilibrium out-of-equilibrium quantum many-particle systems, high-energy physics gravity.