  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.
