Lectures on the functional renormalization group method

By Janos Polonyi. 2001

260 citations recorded by the source corpus.

These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general purpose algorithm to solve strongly coupled quantum field theories. The renormalization group equation of F. Wegner and A. Houghton is shown to resum the loop-expansion. Another version, due to J. Polchinski, is obtained by the method of collective coordinates and can be used for the resummation of the perturbation series. The genuinely non-perturbative evolution equation is obtained by a manner reminiscent of the Schwinger-Dyson equations. Two variants of this scheme are presented where the scale which determines the order of the successive elimination of the modes is extracted from external and internal spaces. The renormalization of composite operators is discussed briefly as an alternative way to arrive at the renormalization group equation. The scaling laws and fixed points are considered from local and global points of view. Instability induced renormalization and new scaling laws are shown to occur in the symmetry broken phase of the scaler theory. The flattening of the effective potential of a compact variable is demonstrated in case of the sine-Gordon model. Finally, a manifestly gauge invariant evolution equation is given for QED.

Subfields: Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/27f69992dcd6e5c0a608030d509f12f4daf55b7a

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In Condensed Matter Physics

1. A. Eichhorn
2. L. Canet
3. W. Metzner
4. N. Dupuis
5. Gianluca Calcagni
6. Jan M. Pawlowski
7. M. Tissier
8. N. Wschebor

In Nuclear and High Energy Physics

1. A. Eichhorn
2. W. Metzner
3. M. Tissier
4. N. Dupuis
5. N. Wschebor
6. L. Canet
7. Jan M. Pawlowski
8. Gianluca Calcagni

Citations in the corpus

• An Asymptotically Safe Guide to Quantum Gravity and Matter (2018, unknown): “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).”
• The nonperturbative functional renormalization group and its applications (2020, background): “of QCD-related reviews that cover some or many of the relevant physics aspects, see [60, 65, 67, 68, 70, 797–805].”
• Cosmology of the Lifshitz universe (2009, background): “These models can be studied with renormalization group (RG) techniques [54, 57, 58, 59, 60].”