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Abstract

In this thesis the real time functional renormalization group is applied to investigate dynamic critical phenomena. In the first part, the established method of the functional renormalization group as a tool for the calculation of real time correlation functions is modified to properly incorporate the thermal equilibrium initial conditions. In the second part, this method is utilized to compute the dynamic critical properties of a system of non-relativistic, bosonic particles. Our result connect to a commonly applied effective description of dynamic critical phenomena. The third part of the thesis extends these calculations to the relativistic O(N) model. The convergence of parts of the truncation as well as the effects of the chosen cutoff function are tested. In the last part, the influence of conserved quantities on the dynamic critical properties of a system is discussed. The dynamic universality class of Model C as a simple, effective approximation of the effects of a conserved quantity on the dynamic critical properties of a system is investigated.