Flow equations for spectral functions at finite external momenta

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In this work we study the spatial-momentum dependence of mesonic spectral functions obtained from the quark-meson model using a recently proposed method to calculate real-time observables at finite temperature and density from the Functional Renormalization Group. This non-perturbative method is thermodynamically consistent, symmetry-preserving and based on an analytic continuation from imaginary to real time on the level of the flow equations for 2-point functions. Results on the spatial-momentum dependence of the pion and sigma spectral function are presented at different temperatures and densities, in particular near the critical endpoint in the phase diagram of the quark-meson model.