Ruprecht Karls Universität Heidelberg

Functional Renormalization
in Quantum Field Theory and Statistical Physics

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The functional renormalisation group (FRG) provides a way of studying field theoretical and statistical-mechanical models systematically as a function of a scale (e.g. a length scale or energy scale). The scale parameter provides an infrared cutoff. The FRG equation is a functional partial differential equation describing the change of the generating functional under variation of the scale parameter. As such, it is an equation that contains the full information about the correlation functions. It therefore allows for exact studies wherever possible and for a systematic improvement of approximations in general. The method has been applied to theories on all energy scales, ranging from ultracold gases to quantum gravity, both in equilibrium and for time-dependent phenomena. In many cases, it has provided a detailed understanding of phase diagrams and physical observables, and thus has made quantitative the general RG idea how effective theories emerge from given fundamental laws. Important contributions to renormalisation group theory have been made by people in Heidelberg, and our institute is one of the major centers worldwide in this area.

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