Functional Renormalization Analytically Continued

We discuss a method to analytically continue functional renormalization group equations from imaginary Matsubara frequencies to the real frequency axis. In this formalism, we investigate the analytic structure of the flowing action and the propagator for a theory of scalar fields with $O(N)$ symmetry. We go on to show how it is possible to derive and solve flow equations for real-time properties such as particle decay widths. Our treatment is fully Lorentz-invariant and enables an improved, self-consistent derivative expansion in Minkowski space.