Aspects of the functional renormalisation group

By Jan M. Pawlowski. 2005

774 citations recorded by the source corpus.

Abstract We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A simple equation for the flow of these relations is provided. The setting includes general flows in the presence of composite operators and their relation to standard flows, an important example being N PI quantities. We discuss optimisation and derive a functional optimisation criterion. Applications deal with the interrelation between functional flows and the quantum equations of motion, general Dyson–Schwinger equations. We discuss the combined use of these functional equations as well as outlining the construction of practical renormalisation schemes, also valid in the presence of composite operators. Furthermore, the formalism is used to derive various representations of modified symmetry relations in gauge theories, as well as to discuss gauge-invariant flows. We close with the construction and analysis of truncation schemes in view of practical optimisation.

Subfields: Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/44f802002ef897b0b89d6206546780662e870455

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. M. Niedermaier
2. Martin Reuter
3. A. Eichhorn
4. J. Rodríguez-Quintero
5. Philippe Boucaud
6. Olivier Pène
7. Jacques Micheli
8. A. Yaouanc

In Nuclear and High Energy Physics

1. A. Eichhorn
2. M. Niedermaier
3. Martin Reuter
4. Jan M. Pawlowski
5. W. Metzner
6. M. Tissier
7. L. Canet
8. N. Dupuis

Citations in the corpus

• Keldysh field theory for driven open quantum systems (2015, background): “Indeed, it has proven a very versatile tool in many different physical context, ranging from quantum dots [234–236], ultracold atoms [233], strongly correlated electrons [237], classical stochastic models [238, 239], quantum chromodynamics [232, 240], to quantum gravity [241].”
• QCD at finite temperature and chemical potential from Dyson–Schwinger equations (2018, neutral): “Closely related to the formalism of Dyson-Schwinger equations is the one for the functional renormalization group (FRG), see [194, 195] and the reviews [196–199].”
• Nonperturbative properties of Yang–Mills theories (2018, neutral): “[124, 138–140].”
• An Asymptotically Safe Guide to Quantum Gravity and Matter (2018, neutral): “For general introductions and reviews (see Berges et al., 2002; Polonyi, 2003; Pawlowski, 2007; Rosten, 2010; Braun, 2012; Delamotte, 2012; Gies, 2012, for gravity, see Reuter and Saueressig, 2012; Nink et al., 2013; Ashtekar et al., 2014; Percacci, 2017; Eichhorn, 2018a).”