Functional Renormalization Group
The functional renormalization group (RG) approaches the study of models of statistical mechanics and quantum field theory by successive integration over degrees of freedom, ordered by a scale parameter that also plays the role of an infrared regulator. The derivative with respect to the scale parameter gives a functional partial differential equation for the generating functions of the theory. This equation is exact, so that the resulting RG flows can in principle studied exactly, and in practice, approximations can be improved systematically.
In our group we apply the fRG method to a variety of systems, ranging from correlated fermions to quantum gravity. The correlated fermion applications focus on models relevant for high-temperature superconductivity, and in particular on two-dimensional models with van Hove singularities (see e.g. C. Husemann and M. Salmhofer, Phys. Rev. B 79, 195125 (2009)). The quantum gravity applications focus on Weinberg's asymptotic safety scenario (see, e.g. Fractal Spacetime Structure in Asymptotically Safe Gravity by O. Lauscher and M. Reuter.
A Germany-wide research network (DFG Forschergruppe FOR 723: Functional Renormalization Group for Correlated Fermions) is coordinated by M. Salmhofer.