Lectures on renormalization and asymptotic safety

Understand

A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects.

• The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety.
• It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization.
• We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross-Neveu model, the nonlinear $\sigma$ model, the sine-Gordon model, and we consider the model of quantum Einstein gravity which seems to show asymptotic safety, too.