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# Master's Thesis

I wrote my master’s thesis under the supervision of Stefan Flörchinger, Michael Scherer and Christof Wetterich at ITP Heidelberg.

## Topic

Functional renormalization group equations are analytically continued 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. The treatment is fully Lorentz-invariant and enables an improved, self-consistent derivative expansion in Minkowski space.